Are Generalized Derivatives Sseful for Generalized Convex Functions?

1998 ◽  
pp. 3-59 ◽  
Author(s):  
Jean-Paul Penot
Keyword(s):  
Convex Functions ◽  
Generalized Derivatives ◽  
Generalized Convex Functions

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.

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.

A generalization of convex functions via support properties

1976 ◽  
Vol 21 (3) ◽  
pp. 341-361 ◽  
Author(s):  
Aharon Ben-Tal ◽  
Adi Ben-Israel
Keyword(s):  
Convex Functions ◽  
Generalized Convex Functions ◽  
Classical Convexity

AbstractWith respect to a given family of functions F, a function is said to be F-convex, if it is supported, at each point, by some member of F. For particular choices of F one obtains the convex functions and the generalized convex functions in the sense of Beckenbach. F-convex functions are characterized and studied, retaining some essential results of classical convexity.

On some generalized convex functions under differentiability

2016 ◽  
Author(s):  
A. K. Das ◽  
Deepmala ◽  
R. Jana
Keyword(s):  
Convex Functions ◽  
Generalized Convex Functions
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