Inequalities of Hermite-Hadamard type for extended $s$-convex functions and applications to means

TL;DR

This paper introduces extended s-convex functions, establishes new Hermite-Hadamard type inequalities for them, and applies these results to derive inequalities involving special means.

Contribution

It presents a novel concept of extended s-convex functions and derives new integral inequalities of Hermite-Hadamard type for this class.

Findings

New inequalities for extended s-convex functions

Applications to inequalities of special means

Extension of classical convexity inequalities

Abstract

In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of special means.