New estimates on generalization of some integral inequalities for s-convex functions and their applications

TL;DR

This paper introduces new estimates for integral inequalities related to s-convex functions, extending classical inequalities like Hadamard, Ostrowski, and Simpson, with applications to real number means.

Contribution

It derives a new identity for differentiable functions and generalizes classical inequalities for functions with s-convex derivatives, providing novel bounds and applications.

Findings

New bounds for Hadamard, Ostrowski, and Simpson inequalities for s-convex functions

Applications to special means of real numbers

Enhanced understanding of inequalities for s-convex functions

Abstract

In this paper, a new identity for differentiable functions is derived. Thus we can obtain new estimates on generalization of Hadamard,Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power are s-convex (in the second sense). Some applications to special means of real numbers are also given.