New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals

İmdat İşcan

doi:10.1155/2014/353924

Abstract

The author obtains new estimates on generalization of Hadamard, Ostrowski, and Simpson type inequalities for Lipschitzian functions via Hadamard fractional integrals. Some applications to special means of positive real numbers are also given.

Highlights

Let real function f be defined on some nonempty interval I of real line R
Following are inequalities which are well known in the literature as Hermite-Hadamard inequality, Ostrowski inequality, and Simpson inequality, respectively
Let f : I ⊆ R → R be a convex function defined on the interval I of real numbers and a, b ∈ I with a < b

Summary

Introduction

Let real function f be defined on some nonempty interval I of real line R. Let f : I ⊆ R → R be a convex function defined on the interval I of real numbers and a, b ∈ I with a < b. We will give definitions of the right-sided and left-sided Hadamard fractional integrals which are used throughout this paper. In [17], Iscan established Hermite-Hadamard’s inequalities for GA-convex functions in Hadamard fractional integral forms as follows. If f is a GA-convex function on [a, b], the following inequalities for fractional integrals hold:. In [17], Iscan obtained a generalization of Hadamard, Ostrowski, and Simpson type inequalities for quasigeometrically convex functions via Hadamard fractional integrals as related to the inequality (8). The author obtains new general inequalities for Lipschitzian functions via Hadamard fractional integrals as related to the inequality (8)

Main Results

Application to Special Means

Conflict of Interests