Some New Hermite-Hadamard type inequalities for s-geometrically convex functions and their applications

TL;DR

This paper introduces new Hermite-Hadamard type integral inequalities tailored for s-geometrically convex functions and demonstrates their applications to calculating special means of positive real numbers.

Contribution

It presents novel integral inequalities for s-geometrically convex functions, expanding the Hermite-Hadamard inequality framework and applying it to mean calculations.

Findings

Established new Hermite-Hadamard type inequalities for s-geometrically convex functions.

Derived applications to special means of positive real numbers.

Extended the scope of convexity-based inequalities.

Abstract

In this paper, some new integral inequalities of Hermite-Hadamard type related to the s-geometrically convex functions are established and some applications to special means of positive real numbers are also given.