On a new class of convex functions and integral inequalities

Abstract

The aim of this paper is to introduce a new extension of convexity called σ -convexity. We show that the class of σ -convex functions includes several other classes of convex functions. Some new integral inequalities of Hermite-Hadamard type are established to illustrate the applications of σ -convex functions. MSC: 26D15; 26D10; 26B25

Some New Integral Inequalities for Ρ–convex Functions

“…Authors of recent decades have studied (1.2) in the premises of newly invented denitions due to motivation of convex function. For applications, generalizations and other aspects of convex functions, HermiteHadamard's inequality and their variant forms, see the references [1] [10]. The motivation of this paper is not only the generalization of the known results by Wu et al in [10] but using our new ideas and techniques we can nd some new interesting results for dierent operators and classes of functions as well.…”

“…The main objective of this article is to generalize the results by Wu et al in [10] using the class of ρconvex functions. We shall also discuss some of its special cases.…”

“…Recently, Wu et al [10] introduced the following new classes of ρconvex sets and ρconvex functions. Denition 1.3.…”

“…Corollary 5.1. Taking α = 1 in Theorem 5, we get ([10], Theorem 3.6).Theorem 6. Suppose that f, h : I → + are two similarly ordered integrable…”

Fractional Hermite-Hadamard Integral Inequalities for a New Class of Convex Functions

“…Recently, in Reference [30], Wu et al introduced a new class of convex sets and convex functions namedσ-convex sets andσ-convex functions which are explained in the following definitions: Definition 1. Letσ ⊆ R be a strictly monotone and continuous function, and denote…”