New inequalities of Ostrowski's type for s-convex functions in the second sense with applications

TL;DR

This paper introduces new Ostrowski-type inequalities for s-convex functions, providing applications to special means and error estimates for the midpoint rule, expanding the theoretical framework of inequalities in analysis.

Contribution

It presents novel Ostrowski-type inequalities for s-convex functions and applies them to derive bounds for special means and midpoint rule errors.

Findings

New inequalities for s-convex functions established

Applications to bounds of special means demonstrated

Error estimates for midpoint formula derived

Abstract

In this paper, we establish some new inequalities of Ostrowski's type for functions whose derivatives in absolute value are the class of s-convex. Some applications for special means of real numbers are also provided. Finally, some error estimates for the midpoint formula are obtained.