New Ostrowski type inequalities for m-convex functions and applications

TL;DR

This paper introduces new Ostrowski type inequalities for m-convex functions, providing bounds and applications to means and error estimates for numerical integration.

Contribution

It presents novel Ostrowski inequalities specifically for m-convex functions and applies these to special means and midpoint error estimates.

Findings

Derived new Ostrowski inequalities for m-convex functions

Applied inequalities to estimate differences between means

Provided error bounds for the midpoint numerical integration

Abstract

In this paper, we establish new inequalities of Ostrowski type for functions whose derivatives in absolute value are m-convex. We also give some applications to special means of positive real numbers. Finally, we obtain some error estimates for the midpoint formula.