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Sabir,Masnita Misiran,Zurni Omar,Rabia Luqman 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.5
In this paper, geometrically convex and $s$-convex functions in third and fourth sense are merged to form ($g,s$)-convex function. Characterizations of ($g,s$)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of ($g,s$)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between ($g,s$)-convex function and previously defined functions. The ($g,s$)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.
QUASI STRONGLY E-CONVEX FUNCTIONS WITH APPLICATIONS
Askar Hussain,Akhlad Iqbal 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.5
In this article, we introduce the quasi strongly E-convex function and pseudo strongly E-convex function on strongly E-convex set which generalizes strongly E-convex function defined by Youness [10]. Some non trivial examples have been constructed that show the existence of these functions. Several interesting properties of these functions have been discussed. An important characterization and relationship of these functions have been established. Furthermore, a nonlinear programming problem for quasi strongly E-convex function has been discussed.
SOME PROPERTIES OF NONCONVEX FUNCTIONS
MUHAMMAD ASLAM NOOR 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.3
In this paper, we introduce and study a new class of convex functions with respect to an arbitrary function, which is called the k-convex function. These functions are nonconvex functions and include the convex function and φ-convex convex as special cases. We study some properties of k-convex functions. It is shown that the minimum of k-convex functions on the k-convex sets can be characterized by a class of variational inequalities, which is called the k-directional variational inequalities. Some open problems are also suggested for future research.
ON TRIGONOMETRICALLY QUASI-CONVEX FUNCTIONS
( Selim Numan ),( İmdat İşcan ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
In this paper, we introduce and study the concept of trigono-metrically quasi-convex function. We prove Hermite-Hadamard type in- equalities for the newly introduced class of functions and obtain some new Hermite-Hadamard inequalities for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is trigonometrically quasi-convex convex. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral the function in the trapezoidal formula.
Superquadratic functions and refinements of some classical inequalities
Senka Banic,Josip Pecaric,Sanja Varosanec 대한수학회 2008 대한수학회지 Vol.45 No.2
Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the Converse and the Reverse Jensen type inequalities, the Giaccardi and the Petrovic type inequalities and Hermite-Hadamard’s inequalities. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given. Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the Converse and the Reverse Jensen type inequalities, the Giaccardi and the Petrovic type inequalities and Hermite-Hadamard’s inequalities. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given.
p-PRECONVEX SETS ON PRECONVEXITY SPACES
Min, Won-Keun The Honam Mathematical Society 2008 호남수학학술지 Vol.30 No.3
In this paper, we introduce the concept of p-preconvex sets on preconvexity spaces. We study some properties for p-preconvex sets by using the co-convexity hull and the convexity hull. Also we introduce and study the concepts of pc-convex function, $p^*c$-convex function, pI-convex function and $p^*I$-convex function.
On harmonic (h,r)-convex functions
Muhammad Aslam Noor,Khalida Inayat Noor,SABAH IFTIKHAR 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.2
In this paper, we introduce a new class of harmonic convex functions with respect to an arbitrary nonnegative function h, which is called harmonic (h, r)-convex functions. We establish some new Hermite- Hadamard integral inequalities for this new class of harmonic (h, r)- convex functions. Our results represent a significant refinement of the known and new special cases. Ideas an techniques of this paper may motivate further research in this dynamic field.
SEMI-PRECONVEX SETS ON PRECONVEXITY SPACES
Min, Won-Keun Korean Mathematical Society 2008 대한수학회논문집 Vol.23 No.2
In this paper, we introduce the concept of the semi-preconvex set on preconvexity spaces. We study some properties for the semi-preconvex set. Also we introduce the concepts of the sc-convex function and $s^*c$-convex function. Finally, we characterize sc-convex functions, $s^*$-convex functions and semi-preconvex sets by using the co-convexity hull and the convexity hull.
p-PRECONVEX SETS ON PRECONVEXITY SPACES
민원근 호남수학회 2008 호남수학학술지 Vol.30 No.3
In this paper, we introduce the concept of p-preconvex sets on preconvexity spaces. We study some properties for p-preconvex sets by using the co-convexity hull and the convexity hull. Also we introduce and study the concepts of pc-convex function, p¤c-convex function, pI-convex function and p¤I-convex function.
On generalized extended beta and hypergeometric functions
Subrat Parida 호남수학회 2024 호남수학학술지 Vol.46 No.2
In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.