On some integral inequalities for s-geometrically convex functions and their applications

TL;DR

This paper develops new integral inequalities for s-geometrically convex functions, extending Hermite-Hadamard type inequalities, and applies these results to derive inequalities involving special means of positive real numbers.

Contribution

Introduces three novel inequalities for differentiable s-geometrically convex functions, generalizing Hermite-Hadamard inequalities and providing applications to means of positive real numbers.

Findings

Established three new inequalities for s-geometrically convex functions.

Extended Hermite-Hadamard inequality to s-geometrically convex functions.

Applied inequalities to derive bounds for special means of positive numbers.

Abstract

In this paper, we establish three inequalities for differentiable s-geometrically and geometrically convex functions which are connected with the famous Hermite-Hadamard inequality holding for convex functions. Some applications to special means of pozitive real numbers are given.