Some New Generalized Integral Inequalities for GA-s-Convex Functions via Hadamard Fractional Integrals

İmdat İşcan,Mustafa Aydin

doi:10.1155/2016/4361806

Abstract

We prove new generalization of Hadamard, Ostrowski, and Simpson inequalities in the framework of GA-s-convex functions and Hadamard fractional integral.

Highlights

Let a real function f be defined on a nonempty interval I of real line R
A function f : [0, ∞) → [0, ∞) is said to be s-convex, or that f belongs to the class Ks2, if f (tx + (1 − t) y) ≤ tsf (x) + (1 − t)s f (y) for all x, y ∈ [0, ∞) and t ∈ [0, 1]
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 a real function f be defined on a nonempty interval I of real line R. The function f is said to be convex on I if inequality f (tx + (1 − t) y) ≤ tf (x) + (1 − t) f (y) holds for all x, y ∈ I and t ∈ [0, 1]. Let f : I ⊆ R → R be a convex function defined on the interval I of real numbers and a, b ∈ I with a < b.

Results

Conclusion