On (h-s)_{1,2}-convex Functions and Hadamard-type Inequalities

TL;DR

This paper introduces new classes of generalized convex functions called (h-s)_{1,2}-convex functions, establishes related Hadamard-type inequalities, and explores their applications to special means.

Contribution

It proposes the (h-s)_{1,2}-convex functions as a novel generalization of convexity and derives new inequalities and applications.

Findings

Established Hadamard-type inequalities for (h-s)_{1,2}-convex functions

Demonstrated applications to special means

Extended the theory of convex functions with new classes

Abstract

In this paper, two new classes of convex functions as a generalization of convexity which is called (h-s)_{1,2}-convex functions are given. We also prove some Hadamard-type inequalities and applications to the special means are given.