scholarly journals Coincidence of Nodes for Generalized Convex Functions

1980 ◽  
Vol 23 (3) ◽  
pp. 317-320
Author(s):  
R. M. Mathsen
Keyword(s):  
Convex Function ◽  
Convergence Theorem ◽  
Convex Functions ◽  
Parameter Family ◽  
Convergence Theorems ◽  
Generalized Convex Functions

In a recent paper [1] I. B. Lazarevic announced an extension of results of L. Tornheim [2; Theorems 2 & 3] concerning points of contact between two distinct members of an n-parameter family and between a member of an n-parameter family and a corresponding convex function. In the proofs of these extensions [1; Theorems 3.1 & 3.2] use is made of Tornheim′s Convergence Theorem [2; Theorem 5]; however this theorem is not correctly applied in [1] since it requires distinct limiting nodes, and that hypothesis necessarily fails in the approach used in [1], In this note proofs of results more general than those in [1] are given independent of convergence theorems.

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 Generalized Convex Functions on Fractal Sets and Two Related Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Huixia Mo ◽  
Xin Sui ◽  
Dongyan Yu
Keyword(s):  
Convex Function ◽  
Real Line ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Generalized Convex Functions ◽  
Fractal Sets ◽  
Hadamard’S Inequality

We introduce the generalized convex function on fractal setsRα  (0<α≤1)of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen’s inequality and generalized Hermite-Hadamard's inequality. Furthermore, some applications are given.

scholarly journals Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
M. Rostamian Delavar ◽  
S. Mohammadi Aslani ◽  
M. De La Sen
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Fejér Inequality ◽  
The Absolute

This paper deals with Hermite-Hadamard-Fejér inequality for (η1,η2)-convex functions via fractional integrals. Some mid-point and trapezoid type inequalities related to Hermite-Hadamard inequality when the absolute value of derivative of considered function is (η1,η2)-convex functions are obtained. Furthermore, a refinement for classic Hermite-Hadamard inequality via fractional integrals is given when a positive (η1,η2)-convex function is increasing.

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

Continuity of h-convex functions

2019 ◽  
Vol 12 (04) ◽  
pp. 1950059
Author(s):  
M. Rostamian Delavar ◽  
S. S. Dragomir
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Continuity Condition

In this paper, a condition which implies the continuity of an [Formula: see text]-convex function is investigated. In fact, any [Formula: see text]-convex function bounded from above is continuous if the function [Formula: see text] satisfies a certain condition which is called pre-continuity condition.

scholarly journals Conformable Fractional Integrals Versions of Hermite-Hadamard Inequalities and Their Generalizations

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Adil Khan ◽  
Yu-Ming Chu ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Gohar Ali
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Montgomery Identity

We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions. We prove new Montgomery identity and by using this identity we obtain generalized Hermite-Hadamard type inequalities.

scholarly journals On Ostrowski-Mercer inequalities for differentiable convex function

2021 ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Ifra Bashir Sial ◽  
Hüseyin BUDAK
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Ostrowski Inequality ◽  
Special Means

In this note, for differentiable convex functions, we prove some new Ostrowski-Mercer inequalities. These inequalities generalize an Ostrowski inequality and related inequalities proved in [3,5]. Some applications to special means are also given.

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