scholarly journals On Semi-(B,G)-Preinvex Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaoling Liu ◽  
D. H. Yuan
Keyword(s):  
Convex Functions ◽  
Generalized Convexity ◽  
Generalized Convex Functions ◽  
Invex Set ◽  
Preinvex Functions ◽  
Generalized Convexities

We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover, we establish relationships between our new generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to common generalized convexity, we obtain results for our new generalized convexities. We extend the existing results in the literature.

Semi-E-Preinvex Functions

2012 ◽  
pp. 677-683
Author(s):  
Yu-Ru Syau ◽  
E. Stanley Lee
Keyword(s):  
Nonlinear Programming ◽  
Euclidean Space ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Dimensional Euclidean Space ◽  
Quasiconvex Functions ◽  
Invex Set ◽  
Preinvex Functions ◽  
The Relationship ◽  
Class Of Functions

A class of functions called semi-E-preinvex functions is defined as a generalization of semi-E-convex functions. Similarly, the concept of semi-E-quasiconvex functions is also generalized to semi-E-prequasiinvex functions. Properties of these proposed classes are studied, and sufficient conditions for a nonempty subset of the n-dimensional Euclidean space to be an E-convex or E-invex set are given. The relationship between semi-E-preinvex and E-preinvex functions are discussed along with results for the corresponding nonlinear programming problems.

scholarly journals On Certain Properties for Two Classes of Generalized Convex Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed S. S. Ali
Keyword(s):  
Convex Functions ◽  
Generalized Convexity ◽  
Generalized Convex Functions ◽  
Hadamard’S Inequality ◽  
Extremum Property

Two classes of generalized convex functions in the sense of Beckenbach are considered. For both classes, we show that the existence of support curves implies their generalized convexity and obtain an extremum property of these functions. Furthermore, we establish Hadamard’s inequality for them.

scholarly journals A Class of SemilocalE-Preinvex Functions and Its Applications in Nonlinear Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Hehua Jiao ◽  
Sanyang Liu ◽  
Xinying Pai
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Convex Functions ◽  
Convex Set ◽  
Basic Properties ◽  
New Class ◽  
Duality Results ◽  
Invex Set ◽  
Preinvex Functions ◽  
Class Of Functions

A kind of generalized convex set, called as local star-shapedE-invex set with respect toη,is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocalE-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocalE-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.

scholarly journals A note on generalized convex functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Syed Zaheer Ullah ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Generalized Convex Functions

Abstract In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate $(\eta _{1}, \eta _{2})$(η1,η2)-convex function and establish its Hermite–Hadamard type inequality.

scholarly journals SOME PROPERTIES OF EXPONENTIALLY PREINVEX FUNCTIONS

2019 ◽  
pp. 941
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Optimality Conditions ◽  
Convex Functions ◽  
New Concepts ◽  
Preinvex Functions

In this paper, we introduce some new concepts of the exponentially preinvex functions. We investigate several properties of the exponentially preinvex functions and discuss their relations with convex functions. Optimality conditions are characterized by a class of variational-like inequalities. Several interesting results characterizing the exponentially preinvex functions are obtained. Results obtained in this paper can be viewed as significant improvement of previously known results.

GENERALIZED h-CONVEXITY ON FRACTAL SETS AND SOME GENERALIZED HADAMARD-TYPE INEQUALITIES

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050021 ◽  
Author(s):  
WENBING SUN
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Generalized Convex Functions ◽  
Text Type ◽  
Fractal Sets ◽  
Type Concept ◽  
Real Linear

In this paper, we introduce the [Formula: see text]-type concept of generalized [Formula: see text]-convex function on real linear fractal sets [Formula: see text], from which the known definitions of generalized convex functions and generalized [Formula: see text]-convex functions are derived, and from this, we obtain generalized Godunova–Levin functions and generalized [Formula: see text]-functions. Some properties of generalized [Formula: see text]-convex functions are discussed. Lastly, some generalized Hadamard-type inequalities of these classes functions are given.

scholarly journals Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Quantum Calculation ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Quantum Integral

In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag–Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities.

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