Ostrowski-type inequalities via h-convex functions with applications to special means

Mevlüt Tunç

doi:10.1186/1029-242x-2013-326

Abstract

In this paper, we establish some new Ostrowski type inequalities for the class of h-convex functions which are super-multiplicative or super-additive and nonnegative. Some applications for special means and PDF's are given.

Highlights

In this paper, we establish some new Ostrowski-type inequalities for absolutely continuous mappings whose first derivatives in absolute value are h-convex and which are super-multiplicative or super-additive
We say that f : I ⊆ R → R is an h-convex function, or that f belongs to the class SX(h, I), if f is nonnegative, and for all x, y ∈ I and t ∈ [, ], we have f tx + ( – t)y ≤ h(t)f (x) + h( – t)f (y)
For recent results related to h-convex functions, see [, – ]

Summary

Introduction

We establish some new Ostrowski-type inequalities for absolutely continuous mappings whose first derivatives in absolute value are h-convex (resp. h-concave) and which are super-multiplicative or super-additive. We say that f : I ⊆ R → R is an h-convex function, or that f belongs to the class SX(h, I), if f is nonnegative, and for all x, y ∈ I and t ∈ [ , ], we have f tx + ( – t)y ≤ h(t)f (x) + h( – t)f (y).

Objectives

Results

Conclusion