


Paper's Title:
The Superstability of the Pexider Type Trigonometric Functional Equation
Author(s):
Gwang Hui Kim and Young Whan Lee
Department of Mathematics, Kangnam
University Yongin, Gyeonggi, 446702, Korea.
ghkim@kangnam.ac.kr
Department of Computer and Information Security
Daejeon University, Daejeon 300716, Korea.
ywlee@dju.ac.kr
Abstract:
The aim of this paper is to investigate the stability
problem for
the Pexider type (hyperbolic) trigonometric functional equation
f(x+y)+f(x+σy)=λg(x)h(y) under the conditions :
f(x+y)+f(x+σy) λg(x)h(y)≤φ(x),
φ(y), and min {φ(x), φ (y)}.
As a consequence, we have generalized the results of stability for
the cosine(d'Alembert), sine, and the Wilson functional equations by J.
Baker, P. Găvruta, R. Badora and R. Ger, Pl.~Kannappan, and G.
H. Kim
Paper's Title:
A Stability of the Gtype Functional Equation
Author(s):
Gwang Hui Kim
Department of Mathematics, Kangnam University
Suwon 449702, Korea.
ghkim@kangnam.ac.kr
Abstract:
We will investigate the stability in the sense of Găvruţă for the Gtype functional equation f(φ(x))=Γ(x)f(x)+ψ(x) and the stability in the sense of Ger for the functional equation of the form f(φ(x))=Γ(x)f(x). As a consequence, we obtain a stability results for Gfunction equation.
Paper's Title:
Evaluation of a New Class of Double Integrals Involving Generalized Hypergeometric Function _{4}F_{3}
Author(s):
Joohyung Kim, Insuk Kim and Harsh V. Harsh
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Korea.
Email: joohyung@wku.ac.kr
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Korea.
Email: iki@wku.ac.kr
Department of Mathematics, Amity School
of Eng. and Tech.,
Amity University Rajasthan
NH11C, Jaipur303002, Rajasthan,
India.
Email: harshvardhanharsh@gmail.com
Abstract:
Very recently, Kim evaluated some double integrals involving a generalized hypergeometric function _{3}F_{2} with the help of generalization of Edwards's wellknown double integral due to Kim, et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. In this research paper we evaluate one hundred double integrals involving generalized hypergeometric function _{4}F_{3} in the form of four master formulas (25 each) viz. in the most general form for any integer. Some interesting results have also be obtained as special cases of our main findings.
Paper's Title:
An Existence of the Solution to Neutral Stochastic Functional Differential Equations Under the Holder Condition
Author(s):
YoungHo Kim
Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnamdo 51140,
Korea.
Email: iyhkim@changwon.ac.kr
Abstract:
In this paper, we show the existence and uniqueness of solution of the neutral stochastic functional differential equations under weakened H\"{o}lder condition, a weakened linear growth condition, and a contractive condition. Furthermore, in order to obtain the existence of a solution to the equation we used the Picard sequence.
Paper's Title:
Viability
Theory And Differential Lanchester Type Models For Combat.
Differential Systems.
Author(s):
G. Isac and A. Gosselin
Department Of
Mathematics, Royal Military College Of Canada,
P.O. Box 17000, Stn Forces, Kingston,
Ontario, Canada K7k 7b4
isacg@rmc.ca
gosselina@rmc.ca
URL:
http://www.rmc.ca/academic/math_cs/isac/index_e.html
URL:
http://www.rmc.ca/academic/math_cs/gosselin/index_e.html
Abstract:
In 1914, F.W. Lanchester proposed several mathematical models based on differential equations to describe combat situations [34]. Since then, his work has been extensively modified to represent a variety of competitions including entire wars. Differential Lanchester type models have been studied from many angles by many authors in hundreds of papers and reports. Lanchester type models are used in the planning of optimal strategies, supply and tactics. In this paper, we will show how these models can be studied from a viability theory stand point. We will introduce the notion of winning cone and show that it is a viable cone for these models. In the last part of our paper we will use the viability theory of differential equations to study Lanchester type models from the optimal theory point of view.
Paper's Title:
On an extension of Edwards's double integral with applications
Author(s):
I. Kim, S. Jun, Y. Vyas and A. K. Rathie
Department of Mathematics Education,
Wonkwang University,
Iksan, 570749,
Republic of Korea.
General Education Institute,
Konkuk University,
Chungju 380701,
Republic of Korea.
Department of Mathematics, School of
Engineering,
Sir Padampat Singhania University,
Bhatewar, Udaipur, 313601, Rajasthan State,
India.
Department of Mathematics,
Vedant College of Engineering and Technology,
(Rajasthan Technical University),
Bundi323021, Rajasthan,
India.
Email: iki@wku.ac.kr
sjun@kku.ac.kr
yashoverdhan.vyas@spsu.ac.in
arjunkumarrathie@gmail.com
Abstract:
The aim of this note is to provide an extension of the well known and useful Edwards's double integral. As an application, new class of twelve double integrals involving hypergeometric function have been evaluated in terms of gamma function. The results are established with the help of classical summation theorems for the series _{3}F_{2} due to Watson, Dixon and Whipple. Several new and interesting integrals have also been obtained from our main findings.
Paper's Title:
Fractional exp(φ(ξ)) Expansion Method and its Application to SpaceTime Nonlinear Fractional Equations
Author(s):
A. A. Moussa and L. A. Alhakim
Department of Management Information
System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
Email: Alaamath81@gmail.com
URL:
https://scholar.google.com/citations?user=ccztZdsAAAAJ&hl=ar
Department of Management Information
System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
Email: Lama2736@gmail.com
URL:
https://scholar.google.com/citations?user=OSiSh1AAAAAJ&hl=ar
Abstract:
In this paper, we mainly suggest a new method that depends on the fractional derivative proposed by Katugampola for solving nonlinear fractional partial differential equations. Using this method, we obtained numerous useful and surprising solutions for the spacetime fractional nonlinear WhithamBroerKaup equations and spacetime fractional generalized nonlinear HirotaSatsuma coupled KdV equations. The solutions obtained varied between hyperbolic, trigonometric, and rational functions, and we hope those interested in the reallife applications of the previous two equations will find this approach useful.
Paper's Title:
On the Hohov Convolution Of The Class S_{p}(α,β)
Author(s):
T. N. Shanmugam and S. Sivasubramanian
Department of Mathematics,
Anna University,
Chennai 600025,
Tamilnadu, India.
shan@annauniv.edu
Department of Mathematics,
Easwari Engineering College,
Chennai600089,
Tamilnadu, India,
sivasaisastha@rediffmail.com
Abstract:
Let F(a,b;c;z) be the Gaussian hypergeometric function and I_{a,b;c}(f)=zF(a,b;c;z)*f(z) be the Hohlov operator defined on the class A of all normalized analytic functions. We determine conditions on the parameters a,b,c such that I_{a,b;c}(f) will be in the class of parabolic starlike functions S_{p}(α,β). Our results extend several earlier results.
Paper's Title:
Komatu Integral Transforms of Analytic Functions Subordinate to Convex Functions
Author(s):
T. N. Shanmugam and C. Ramachandran
Department of Mathematics, College of Engineering,
Anna University, Chennai600 025, Tamilnadu,
India
shan@annauniv.edu
Department of Mathematics, College of Engineering,
Anna University, Chennai600 025, Tamilnadu,
India
crjsp2004@yahoo.com
Abstract:
In this paper, we consider the class A of the functions f(z) of the form
which are analytic in an open disk
and study certain subclass of the class A, for which
has some property. Certain inclusion and the closure properties like convolution with convex univalent function etc. are studied.
Paper's Title:
Approximation of an AQCQFunctional Equation and its Applications
Author(s):
Choonkil Park and Jung Rye Lee
Department of Mathematics,
Research Institute for Natural Sciences,
Hanyang University, Seoul 133791,
Korea;
Department of Mathematics,
Daejin University,
Kyeonggi 487711,
Korea
baak@hanyang.ac.kr
jrlee@daejin.ac.kr
Abstract:
This paper is a survey on the generalized HyersUlam stability of an AQCQfunctional equation in several spaces. Its content is divided into the following sections:
1. Introduction and preliminaries.
2. Generalized HyersUlam stability of an AQCQfunctional equation in Banach spaces: direct method.
3. Generalized HyersUlam stability of an AQCQfunctional equation in Banach spaces: fixed point method.
4. Generalized HyersUlam stability of an AQCQfunctional equation in random Banach spaces: direct method.
5. Generalized HyersUlam stability of an AQCQfunctional equation in random Banach spaces: fixed point method.
6. Generalized HyersUlam stability of an AQCQfunctional equation in nonArchimedean Banach spaces: direct method.
7. Generalized HyersUlam stability of an AQCQfunctional equation in nonArchimedean Banach spaces: fixed point method.
Paper's Title:
On a New Class of Eulerian's Type Integrals Involving Generalized Hypergeometric Functions
Author(s):
Sungtae Jun, Insuk Kim and Arjun K. Rathie
General Education Institute,
Konkuk University, Chungju 380701,
Republic of Korea.
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Republic of Korea.
Department of Mathematics,
Vedant College of Engineering and Technology (Rajasthan Technical University),
Bundi323021, Rajasthan,
India.
Email: sjun@kku.ac.kr, iki@wku.ac.kr, arjunkumarrathie@gmail.com
Abstract:
Very recently MasjedJamei and Koepf established interesting and useful generalizations of various classical summation theorems for the _{2}F_{1}, _{3}F_{2}, _{4}F_{3}, _{5}F_{4} and _{6}F_{5} generalized hypergeometric series. The main aim of this paper is to establish eleven Eulerian's type integrals involving generalized hypergeometric functions by employing these theorems. Several special cases have also been given.
Paper's Title:
Norm Estimates for the Difference between Bochner’s Integral and the Convex Combination of Function’s Values
Author(s):
P. Cerone, Y.J. Cho, S.S. Dragomir, J.K. Kim, and S.S. Kim
School of
Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
pietro.cerone@vu.edu.au
URL:
http://rgmia.vu.edu.au/cerone/index.html
Department of
Mathematics Education, College of Education,
Gyeongsang National University, Chinju 660701, Korea
yjcho@nongae.gsnu.ac.kr
School of
Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
sever.dragomir@vu.edu.au
URL:
http://rgmia.vu.edu.au/SSDragomirWeb.html
Department of
Mathematics, Kyungnam University,
Masan,, Kyungnam 631701, Korea
jongkyuk@kyungnam.ac.kr
Department of
Mathematics, Dongeui University,
Pusan 614714, Korea
sskim@dongeui.ac.kr
Abstract:
Norm estimates are developed between the Bochner integral of a vectorvalued function in Banach spaces having the RadonNikodym property and the convex combination of function values taken on a division of the interval [a, b].
Paper's Title:
Algebraic Approach to the Fractional Derivatives
Author(s):
Kostadin Trenčevski and Živorad Tomovski
Institute of Mathematics,
St. Cyril and Methodius University,
P.O. Box 162, 1000 Skopje,
Macedonia
kostatre@iunona.pmf.ukim.edu.mk
tomovski@iunona.pmf.ukim.edu.mk
URL:http://www.pmf.ukim.edu.mk
Abstract:
In this paper we introduce an alternative definition of the fractional derivatives and also a characteristic class of so called ideal functions, which admit arbitrary fractional derivatives (also integrals). Further some ideal functions are found, which lead to representations of the Bernoulli and Euler numbers B_{k} and E_{k} for any real number k, via fractional derivatives of some functions at x=0.
Paper's Title:
Stability of a Mixed Additive, Quadratic and Cubic Functional Equation In QuasiBanach Spaces
Author(s):
A. Najati and F. Moradlou
Department of Mathematics, Faculty of Sciences,
University of Mohaghegh Ardabili, Ardabil,
Iran
a.nejati@yahoo.com
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz,
Iran
moradlou@tabrizu.ac.ir
Abstract:
In this paper we establish the general solution of a mixed additive, quadratic and cubic functional equation and investigate the HyersUlamRassias stability of this equation in quasiBanach spaces. The concept of HyersUlamRassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297300.
Paper's Title:
On the Generalized Stability and Asymptotic Behavior of Quadratic Mappings
Author(s):
HarkMahn Kim, SangBaek Lee and Eunyoung Son
Department of Mathematics
Chungnam National University
Daejeon,
305764,
Republic of Korea
hmkim@cnu.ac.kr
Abstract:
We extend the stability of quadratic mappings to the stability of general quadratic mappings with several variables, and then obtain an improved asymptotic property of quadratic mappings on restricted domains.
Paper's Title:
Shape Diagrams for 2D Compact Sets  Part III: Convexity Discrimination for Analytic and Discretized Simply Connected Sets.
Author(s):
S. Rivollier, J. Debayle and J.C. Pinoli
Ecole Nationale Supérieure des Mines de SaintEtienne,
CIS  LPMG, UMR CNRS
5148,
158 cours Fauriel,
42023 SaintEtienne Cedex 2, France.
rivollier@emse.fr;
debayle@emse.fr; pinoli@emse.fr
Abstract:
Shape diagrams are representations in the Euclidean plane introduced to study 3dimensional and 2dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow twentytwo shape diagrams to be built. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these twentytwo shape diagrams. The two first parts of this study are published in previous papers 8,9. They focus on analytic compact convex sets and analytic simply connected compact sets, respectively. The purpose of this paper is to present the third part, by focusing on the convexity discrimination for analytic and discretized simply connected compact sets..
Paper's Title:
Inclusion Properties of a Certain Subclass of Strongly CloseToConvex Functions
Author(s):
S. M. Khairnar and M. More
Department of Mathematics,
Maharashtra Academy of Engineerring,
Alandi 412 105, Pune, Maharashtra,
INDIA.
smkhairnar2007@gmail.com,
meenamores@gmail.com.
Abstract:
The purpose of this paper is to derive some inclusion and argument properties of a new subclass of strongly closetoconvex functions in the open unit disc. We have considered an integral operator defined by convolution involving hypergeometric function in the subclass definition. The subclass also extends to the class of αspirallike functions of complex order.
Paper's Title:
Stability Problems for Generalized Additive Mappings and EulerLagrange Type Mappings
Author(s):
M. Todoroki, K. Kumahara, T. Miura and S.E. Takahasi
The Open University of Japan,
Chiba, 2618586,
Japan
tomamiyu3232@sky.sannet.ne.jp
kumahara@ouj.ac.jp
Yamagata University,
Yonezawa 9928510,
Japan
miura@yz.yamagatau.ac.jp
Toho University, Yamagata University,
Chiba, 2730866,
Japan
sin_ei1@yahoo.co.jp
Abstract:
We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of EulerLagrange type mappings obtained by H. M. Kim, K. W. Jun and J. M. Rassias.
Paper's Title:
Some Distortion and Other Properties Associated with a Family of the nFold Symmetric Koebe Type Functions
Author(s):
H. M. Srivastava, N. Tuneski and E. GeorgievaCelakoska
Department of Mathematics and Statistics,
University of Victoria,
Victoria, British Columbia V8W 3R4,
Canada
Faculty of Mechanical Engineering, St.
Cyril and Methodius University,
Karpo'v s II b.b., MK1000 Skopje,
Republic of Macedonia
Abstract:
In a recent work by Kamali and Srivastava [5], a certain family of the nfold symmetric Koebe type functions was introduced and studied systematically. In an earlier investigation, Eguchi and Owa [4] had considered its special case when n=1 (see also [10]). Here, in our present sequel to these earlier works, this general family of the nfold symmetric Koebe type functions is studied further and several distortion theorems and such other properties as the radii of spirallikeness, the radii of starlikeness and the radii of convexity, which are associated with this family of the nfold symmetric Koebe type functions, are obtained. We also provide certain criteria that embed this family of the nfold symmetric Koebe type functions in a function class G_{λ} which was introduced and studied earlier by Silverman [7].
Paper's Title:
On Reformations of 2Hilbert Spaces
Author(s):
M. Eshaghi Gordji, A. Divandari, M. R. Safi and Y. J. Cho
Department of Mathematics, Semnan
University,
P.O. Box 35195363, Semnan,
Iran
meshaghi@semnan.ac.ir, madjid.eshaghi@gmail.com
Department of Mathematics, Semnan
University,
Iran
Department of Mathematics, Semnan
University,
Iran
safi@semnan.ac.ir, SafiMohammadReza@yahoo.com
Department of Mathematics Education and
the RINS,
Gyeongsang National University
Chinju 660701,
Korea
Abstract:
In this paper, first, we introduce the new concept of (complex) 2Hilbert spaces, that is, we define the concept of 2inner product spaces with a complex valued 2inner product by using the 2norm. Next, we prove some theorems on Schwartz's inequality, the polarization identity, the parallelogram laws and related important properties. Finally, we give some open problems related to 2Hilbert spaces.
Paper's Title:
A Note on Divergent Fourier Series and λPermutations
Author(s):
A. Castillo, J. Chavez and H. Kim
Tufts University,
Department of Mathematics,
Medford, MA 02155,
USA
Email: angel.castillo@tufts.edu
Texas Tech University,
Department of Mathematics and Statistics,
Lubbock, TX 79409,
USA
Email: josechavez5@my.unt.edu
University of MichiganDearborn,
Department of Mathematics and Statistics,
Dearborn, MI 48128,
USA.
Email: khyejin@umich.edu
Abstract:
We present a continuous function on [π,π] whose Fourier series diverges and it cannot be rearranged to converge by a λpermutation.
Paper's Title:
The Functional Equation With an Exponential Polynomial Solution and its Stability
Author(s):
Young Whan Lee^{1}, Gwang Hui Kim^{2*}, and Jeong Il Kim^{3}
^{1}Department of Computer
Hacking and Information Security,
College of Engineering, Daejeon University,
Daejeon, 34520,
Korea(Republic of).
Email: ywlee@dju.ac.kr
^{2}Department of Mathematics,
Kangnam University,
Yongin, Gyeonggi, 16979,
Korea(Republic of).
Email: ighkim@kangnam.ac.kr
^{3}Department of Statistics,
Daejeon University,
Daejeon 34520,
Korea(Republic of).
Email: jlkim@dju.ac.kr
Abstract:
In this paper, we prove that the unique continuous solution of the functional equation
is
where p_{n}(x) is a polynomial with degree n and
We also obtain the superstability and stability of the functional equation with the following forms, respectively:
and
Paper's Title:
Convergence Speed of Some Random ImplicitKirktype Iterations for Contractivetype Random Operators
Author(s):
H. Akewe, K.S. Eke
Department of Mathematics,
Covenant University,
Canaanland, KM 10, Idiroko Road, P. M. B. 1023, Ota, Ogun State,
Nigeria.
Email: hudson.akewe@covenantuniversity.edu.ng,
kanayo.eke@covenantuniversity.edu.ng
Abstract:
The main aim of this paper is to introduce a stochastic version of multistep type iterative scheme called a modified random implicitKirk multistep iterative scheme and prove strong convergence and stability results for a class of generalized contractivetype random operators. The rate of convergence of the random iterative schemes are also examined through an example. The results show that our new random implicit kirk multistep scheme perform better than other implicit iterative schemes in terms of convergence and thus have good potentials for further applications in equilibrium problems in computer science, physics and economics.
Paper's Title:
The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations
Author(s):
Alexandru Mihai Bica
Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro
Abstract:
We present here a numerical method for first order delay ordinary differential equations, which use the Banach's fixed point theorem, the sequence of successive approximations and the trapezoidal quadrature rule. The error estimation of the method uses a recent result of P. Cerone and S.S. Dragomir about the remainder of the trapezoidal quadrature rule for Lipchitzian functions and for functions with continuous first derivative.
Paper's Title:
Logarithmically complete monotonicity properties for the gamma functions
Author(s):
ChaoPing Chen and Feng Qi
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010,
China.
chenchaoping@hpu.edu.cn
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010,
China.
qifeng@hpu.edu.cn
fengqi618@member.ams.org
Abstract:
Some logarithmically completely monotonic functions involving the gamma functions are presented. As a consequence, some known results are proved and refined.
Paper's Title:
On Sandwich Theorems for Certain Subclass of Analytic Functions Involving DziokSrivastava Operator
Author(s):
T. N. Shanmugam, M. P. Jeyarama and A. Singaravelu
Department of Mathematics
College of Engineering, Anna University
Chennai  600 025,
India
drtns2001@yahoo.com
Department of Mathematics
Easwari Engineering College
Ramapuram, Chennai  600089
Tamilnadu, India
jeyaramanmp@yahoo.co.i
Department of Mathematics
Valliammai Engineering College
Chennai  603203
Tamilnadu, India.
asing59@yahoo.com
Abstract:
The purpose of this present paper is to derive some subordination and superordination results for certain normalized analytic functions in the open unit disk, acted upon by DziokSrivastava operator. Relevant connections of the results, which are presented in this paper, with various known results are also considered.
Paper's Title:
Some Inequalities for a Certain Class of Multivalent Functions Using Multiplier Transformation
Author(s):
K. Suchithra, B. Adolf Stephen, A. Gangadharan and S. Sivasubramanian
Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai  602105,
India.
suchithravenkat@yahoo.co.in
Department Of Mathematics,
Madras Christian College
Chennai  600059,
India.
adolfmcc2003@yahoo.co.in
Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai  602105,
India.
ganga@svce.ac.in
Department Of Mathematics,
Easwari Engineering College
Ramapuram, Chennai  600089,
India.
ganga@svce.ac.in
Abstract:
The object of the present paper is to derive several inequalities associated with differential subordinations between analytic functions and a linear operator defined for a certain family of pvalent functions, which is introduced here by means of a family of extended multiplier transformations. Some special cases and consequences of the main results are also considered.
Paper's Title:
On Stan Ulam and his Mathematics
Author(s):
Krzysztof Ciesielski and Themistocles M. Rassias
Mathematics Institute, Jagiellonian University,
Łjasiewicza 6,
30348 Kraków,
Poland
Department of Mathematics. National Technical University of Athens,
Zografou
Campus, 15780 Athens,
Greece
Krzysztof.Ciesielski@im.uj.edu.pl
trassias@math.ntua.gr
Abstract:
In this note we give a glimpse of the curriculum vitae of Stan Ulam, his personality and some of the mathematics he was involved in.
Paper's Title:
Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions
Author(s):
Árpád Száz
Institute of Mathematics, University of Debrecen,
H4010 Debrecen,
Pf. 12,
Hungary
szaz@math.klte.hu
Abstract:
By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.
Paper's Title:
Ulam Stability of Reciprocal Difference and Adjoint Functional Equations
Author(s):
K. Ravi, J. M. Rassias and B. V. Senthil Kumar
Department of Mathematics,
Sacred Heart College, Tirupattur  635601,
India
Pedagogical Department E. E.,
Section of Mathematics and Informatics,
National and Capodistrian University of Athens,
4, Agamemnonos Str., Aghia Paraskevi,
Athens, Attikis 15342,
GREECE
Department of Mathematics,
C.Abdul Hakeem College of Engineering and
Technology, Melvisharam  632 509, India
shckavi@yahoo.co.in
jrassias@primedu.uoa.gr
bvssree@yahoo.co.in
Abstract:
In this paper, the reciprocal difference functional equation (or RDF equation) and the reciprocal adjoint functional equation (or RAF equation) are introduced. Then the pertinent Ulam stability problem for these functional equations is solved, together with the extended Ulam (or Rassias) stability problem and the generalized Ulam (or UlamGavrutaRassias) stability problem for the same equations.
Paper's Title:
Subordination Results Associated with Hadamard Product
Author(s):
S. Sivasubramanian, C. Ramachandran and B. A. Frasin
Department of Mathematics,
University College of Engineering,
Anna University,
Saram604 307,
India
Department of Mathematics,
University College of Engineering,
Anna University,
Villupuram,
India
Department of Mathematics,
Al alBayt University,
P.O. Box: 130095 Mafraq,
Jordan
Abstract:
In the present investigation, we consider an unified class of functions of complex order using Hadamard's convolution. We obtain a necessary and sufficient condition for functions to be in these classes.
Paper's Title:
On the Three Variable Reciprocity Theorem and Its Applications
Author(s):
D. D. Somashekara and D. Mamta
Department of Studies in Mathematics,
University of Mysore,
Manasagangotri, Mysore570 006
India
dsomashekara@yahoo.com
Department of Mathematics,
The National Institute of Engineering,
Mysore570 008,
India
mathsmamta@yahoo.com
Abstract:
In this paper we show how the three variable reciprocity theorem can be easily derived from the well known two variable reciprocity theorem of Ramanujan by parameter augmentation. Further we derive some qgamma, qbeta and etafunction identities from the three variable reciprocity theorem.
Paper's Title:
Applications of the Structure Theorem of (w_{1},w_{2})Tempered Ultradistributions
Author(s):
Hamed M. Obiedat and Lloyd E. Moyo
Department of Mathematics,
Hashemite University,
P.O.Box 150459, Zarqa13115,
Jordan.
Email: hobiedat@hu.edu.j
Department of Mathematics, Computer
Science & Statistics,
Henderson State University,
1100 Henderson Street, Arkadelphia, AR 71999,
USA.
Email: moyol@hsu.edu
Abstract:
Using a previously obtained structure theorem for (w_{1}, w_{2})tempered ultradistributions, we prove that these ultradistributions can be represented as initial values of solutions of the heat equation.
Paper's Title:
Inequalities for Discrete FDivergence Measures: A Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated fdivergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of KullbackLeibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the fdivergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.
Paper's Title:
On Commutator of Aluthge Transforms and FugledePutnam Property
Author(s):
(Manzar Maleki, Ali Reza Janfada and Seyed Mohammad Sadegh Nabavi Sales
International Campus, Faculty of
Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad,
Iran.
Email: manzar.maleki@gmail.com
Faculty of Mathematics and Statistics,
Department of Mathematics,
University of Birjand,
P. O. Box 414, Birjand 9717851367,
Iran.
Email: ajanfada@birjand.ac.ir
Department of Pure Mathematics, Hakim
Sabzevari University,
P.O. Box 397, Sabzevar,
Iran.
Email: sadegh.nabavi@hsu.ac.ir
Abstract:
We deal with the wellknown FugledePutnam theorem and related FPproperty. We show that if (A,B) has the FPproperty, then so has where 0≤ t_{1},t_{2}≤1 are arbitrary. We first prove that if and only if AX=XB for all X, whenever (A,B) has the FPproperty. We prove some similar results for instead of $ as well. Also we introduce the sequence of generalized iterations of Aluthge transform of operators and express some results for this notion associated to the FPproperty.
Paper's Title:
On Euler's First Transformation Formula for khypergeometric Function
Author(s):
Sungtae Jun and Insuk Kim
General Education Institute,
Konkuk University, Chungju 380701,
Republic of Korea.
Email: sjun@kku.ac.kr
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Republic of Korea.
Email: iki@wku.ac.kr
Abstract:
Mubeen et al. obtained Kummer's first transformation for the khypergeometric function. The aim of this note is to provide the Eulertype first transformation for the khypergeometric function. As a limiting case, we recover the results of Mubeen et al. In addition to this, an alternate and easy derivation of Kummer's first transformation for the khypergeometric function is also given.
Paper's Title:
On Certain Classes of Harmonic Univalent Functions Based on Salagean Operator
Author(s):
G. Murugusundaramoorthy, Thomas Rosy, and B. A. Stephen
Department of Applied Mathematics and Informatics,
Department of Mathematics, Vellore Institute of Technology,
Deemed University, Vellore  632014, India.
gmsmoorthy@yahoo.com
Department of Applied Mathematics and Informatics,
Department of Mathematics, Madras Christian College,
Chennai  600059, India.
drthomasrosy@rediffmail.com
Abstract:
We define and investigate a class of complexvalued harmonic univalent functions of the form f = h + g using Salagean operator where h and g are analytic in the unit disc U = { z : z < 1 }. A necessary and sufficient coefficient conditions are given for functions in these classes. Furthermore, distortion theorems, inclusion relations, extreme points, convolution conditions and convex combinations for this family of harmonic functions are obtained.
Paper's Title:
Refinement Inequalities Among Symmetric Divergence Measures
Author(s):
Inder Jeet Taneja
Departamento de Matemática,
Universidade Federal de Santa Catarina, 88.040900
Florianópolis, Sc, Brazil
taneja@mtm.ufsc.br
URL: http://www.mtm.ufsc.br/~taneja
Abstract:
There are three classical divergence measures in the literature on information theory and statistics, namely, JeffryesKullbackLeiber’s Jdivergence, SibsonBurbeaRao’s Jensen Shannon divegernce and Taneja’s arithemtic  geometric mean divergence. These bear an interesting relationship among each other and are based on logarithmic expressions. The divergence measures like Hellinger discrimination, symmetric χ^{2}−divergence, and triangular discrimination are not based on logarithmic expressions. These six divergence measures are symmetric with respect to probability distributions. In this paper some interesting inequalities among these symmetric divergence measures are studied. Refinements of these inequalities are also given. Some inequalities due to Dragomir et al. [6] are also improved.
Paper's Title:
Iterative Approximation of Common Fixed Points of a Finite Family of Asymptotically Hemicontractive Type Mappings
Author(s):
JuiChi Huang
Center for General Education,
Northern Taiwan Institute of Science and Technology,
Peito, Taipei,
Taiwan, 11202, R.O.C.
juichi@ntist.edu.tw
Abstract:
In this paper, we prove that the sequence of
the modified IshikawaXu,
IshikawaLiu, MannXu and MannLiu iterative types of a finite family of
asymptotically hemicontractive type mappings converges strongly to a common
fixed point of the family in a real puniformly convex Banach space with
p>1. Our results improve and extend some recent results.
Paper's Title:
Generalizations of HermiteHadamard's Inequalities for LogConvex Functions
Author(s):
AiJun Li
School of Mathematics and Informatics,
Henan Polytechnic University,
Jiaozuo City, Henan Province,
454010, China.
liaijun72@163.com
Abstract:
In this article, HermiteHadamard's inequalities are extended in terms of the weighted power mean and logconvex function. Several refinements, generalizations and related inequalities are obtained.
Paper's Title:
On a Method of Proving the HyersUlam Stability of Functional Equations on Restricted Domains
Author(s):
Janusz Brzdęk
Department of Mathematics
Pedagogical University Podchorąźych 2,
30084 Kraków,
Poland
jbrzdek@ap.krakow.pl
Abstract:
We show that generalizations of some (classical) results on the HyersUlam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable
Paper's Title:
Harmonic Functions with Positive Real Part
Author(s):
Sïbel Yalçin
Uludag Universitesi,
Fen Edebiyat Fakultesi, Matematik Bolumu,
16059 Bursa,
Turkey
Abstract:
In this paper, the class of harmonic functions f=h+{g} with positive real part and normalized by f(ζ )=1, (ζ<1) is studied, where h and g are analytic in U={z:z<1}. Some properties of this class are searched. Sharp coefficient relations are given for functions in this class. On the other hand, the author make use of Alexander integral transforms of certain analytic functions (which are starlike with respect to f(ζ)) with a view to investigating the construction of sense preserving, univalent and close to convex harmonic functions.
Paper's Title:
Some Identities for Ramanujan  Göllnitz  Gordon Continued fraction
Author(s):
M. S. Mahadeva Naika, B. N. Dharmendra and S. Chandan Kumar
Department of Mathematics,
Bangalore University,
Central College Campus,
Bangalore560 001,
INDIA
Department of Mathematics,
Maharani's Science College for Women,
J. L. B. Road, Mysore570 001,
INDIA
Abstract:
In this paper, we obtain certain PQ etafunction identities, using which we establish identities providing modular relations between RamanujanGöllnitzGordon continued fraction H(q) and H(q^n) for n= 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 17, 19, 23, 25, 29 and 55.
Paper's Title:
Hyponormal and KQuasiHyponormal Operators On SemiHilbertian Spaces
Author(s):
Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali
Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
Email:
sididahmed@ju.edu.sa
Mathematics Department, Faculty of
Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
Email:
benali4848@gmail.com
Abstract:
Let H be a Hilbert space and let A be a positive bounded operator on H. The semiinner product < uv>_{A}:=<Auv>, u,v ∈ H induces a seminorm  ._{A} on H. This makes H into a semiHilbertian space. In this paper we introduce the notions of hyponormalities and kquasihyponormalities for operators on semi Hilbertian space (H,._{A}), based on the works that studied normal, isometry, unitary and partial isometries operators in these spaces. Also, we generalize some results which are already known for hyponormal and quasihyponormal operators. An operator T ∈ B_{A} (H) is said to be (A, k)quasihyponormal if
Paper's Title:
Robust Error Analysis of Solutions to Nonlinear Volterra Integral Equation in L^{p} Spaces
Author(s):
Hamid Baghani, Javad FarokhiOstad and Omid Baghani
Department of Mathematics, Faculty of
Mathematics,
University of Sistan and Baluchestan, P.O. Box 98135674, Zahedan,
Iran.
Email:
h.baghani@gmail.com
Department of Mathematics, Faculty of
Basic Sciences,
Birjand University of Technology, Birjand,
Iran.
Email: j.farrokhi@birjandut.ac.ir
Department of Mathematics and Computer
Sciences,
Hakim Sabzevari University, P.O. Box 397, Sabzevar,
Iran.
Email:
o.baghani@gmail.com
Abstract:
In this paper, we propose a novel strategy for proving an important inequality for a contraction integral equations. The obtained inequality allows us to express our iterative algorithm using a "for loop" rather than a "while loop". The main tool used in this paper is the fixed point theorem in the Lebesgue space. Also, a numerical example shows the efficiency and the accuracy of the proposed scheme.
Paper's Title:
The Dynamics of an Ebola Epidemic Model with Quarantine of Infectives
Author(s):
Eliab Horub Kweyunga
Department of Mathematics,
Kabale University,
P.O.Box 317, Kabale,
Uganda.
Email: hkweyunga@kab.ac.ug
Abstract:
The recurrent outbreaks of ebola in Africa present global health challenges. Ebola is a severe, very fatal disease with case fatality rates of up to 90%. In this paper, a theoretical deterministic model for ebola epidemic with quarantine of infectives is proposed and analyzed. The model exhibits two equilibria; the disease free and endemic equilibrium points. The basic reproduction number, R_{0}, which is the main threshold, is obtained and the stability of the equilibrium points established. Using parameter values drawn from the 2014 West Africa ebola outbreak, a numerical simulation of the model is carried out. It is found that the dynamics of the model are completely determined by R_{0} and that a quarantine success rate of at least 70% is sufficient to contain the disease outbreak.
Paper's Title:
Some fixed point results in partial Smetric spaces
Author(s):
M. M. Rezaee, S. Sedghi, A. Mukheimer, K. Abodayeh, and Z. D. Mitrovic
Department of Mathematics, Qaemshahr
Branch,
Islamic Azad University, Qaemshahr,
Iran.
Email: Rezaee.mohammad.m@gmail.com
Department of Mathematics, Qaemshahr
Branch,
Islamic Azad University, Qaemshahr,
Iran.
Email: sedghi.gh@qaemiau.ac.ir
Department of Mathematics and General
Sciences,
Prince Sultan University, Riyadh,
KSA.
Email: mukheimer@psu.edu.sa
Department of Mathematics and General
Sciences,
Prince Sultan University, Riyadh,
KSA.
Email: kamal@psu.edu.sa
Nonlinear Analysis Research Group,
Faculty of Mathematics and Statistics,
Ton Duc Thang University, Ho Chi Minh City,
Vietnam.
Email: zoran.mitrovic@tdtu.edu.vn
Abstract:
We introduce in this article a new class of generalized metric spaces, called partial Smetric spaces. In addition, we also give some interesting results on fixed points in the partial Smetric spaces and some applications.
Paper's Title:
ψ(m,q)Isometric Mappings on Metric Spaces
Author(s):
Sid Ahmed Ould Beinane, Sidi Hamidou Jah and Sid Ahmed Ould Ahmed Mahmoud
Mathematical Analysis and Applications,
Mathematics Department, College of Science,
Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
Email: beinane06@gmail.com
Department of Mathematics, College of
Science Qassim University,
P.O. Box 6640, Buraydah 51452,
Saudi Arabia.
Email: jahsiidi@yahoo.fr
Mathematical Analysis and Applications,
Mathematics Department, College of Science, Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
Email: sidahmed@ju.edu.sa,
sidahmed.sidha@gmail.com
Abstract:
The concept of (m,p)isometric operators on Banach space was extended to
(m,q)isometric mappings on general metric spaces in [6].
This paper is devoted to define the concept of
ψ(m, q)isometric, which is the
extension of A(m, p)isometric operators on Banach spaces introduced in [10].
Let T,ψ: (E,d) > (E, d) be two mappings.
For some positive integer m and q ∈ (0,∞).
T is said to be an ψ(m,q)isometry,
if for all y,z ∈ E,
Paper's Title:
Sharp Inequalities Between Hölder and Stolarsky Means of Two Positive Numbers
Author(s):
M. Bustos Gonzalez and A. I. Stan
The University of Iowa,
Department of Mathematics,
14 MacLean Hall,
Iowa City, Iowa,
USA.
Email:
margaritabustosgonzalez@uiowa.edu
The Ohio State University at Marion,
Department of Mathematics,
1465 Mount Vernon Avenue,
Marion, Ohio,
USA.
Email: stan.7@osu.edu
Abstract:
Given any index of the Stolarsky means, we find the greatest and least indexes of the H\"older means, such that for any two positive numbers, the Stolarsky mean with the given index is bounded from below and above by the Hölder means with those indexes, of the two positive numbers. Finally, we present a geometric application of this inequality involving the FermatTorricelli point of a triangle.
Paper's Title:
Generalized Von NeumannJordan Constant for Morrey Spaces and Small Morrey Spaces
Author(s):
H. Rahman and H. Gunawan
Department of Mathematics,
Islamic State University Maulana Malik Ibrahim Malang,
Jalan Gajayana No.50,
Indonesia.
Email: hairur@mat.uinmalang.ac.id
Analysis and Geometry Group,
Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
Email: hgunawan@math.itb.ac.id
URL:
http://personal.fmipa.itb.ac.id/hgunawan/
Abstract:
In this paper we calculate some geometric constants for Morrey spaces and small Morrey spaces, namely generalized Von NeumannJordan constant, modified Von NeumannJordan constants, and Zbaganu constant. All these constants measure the uniformly nonsquareness of the spaces. We obtain that their values are the same as the value of Von NeumannJordan constant for Morrey spaces and small Morrey spaces.
Paper's Title:
Algorithms for Nonlinear Problems Involving Strictly Pseudocontractive Mappings
Author(s):
Mathew Olajiire Aibinu^{1}, Surendra Colin Thakur^{2}, Sibusiso Moyo^{3}
^{1}Institute for Systems Science
& KZN ESkill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
^{1}DSINRF
Centre of Excellence in Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Email: moaibinu@yahoo.com
mathewa@dut.ac.za
^{2} KZN ESkill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
Email: thakur@dut.ac.za
^{3}Institute for Systems Science & Office of the DVC Research,
Innovation & Engagement Milena Court,
Durban University of Technology,
Durban 4000,
South Africa.
Email: dvcrie@dut.ac.za
Abstract:
The puzzles in approximating a fixed point of nonlinear problems involving the class of strictly pseudocontractive mappings are conquered in this paper through viscosity implicit rules. Using generalized contraction mappings, a new viscosity iterative algorithm which is implicit in nature is proposed and analysed in Banach spaces for the class of strictly pseudocontractive mappings. The computations and analysis which are used in the proposed scheme are easy to follow and this gives rooms for a broad application of the scheme. It is obtained that the proposed iterative algorithm converges strongly to a fixed point of a μstrictly pseudocontractive mapping which also solves a variational inequality problem. The result is also shown to hold for finite family of strictly pseudocontractive mappings. A numerical example is given to show the skillfulness of the proposed scheme and its implementation.
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