Inequalities for mathbb{B}-convex functions via generalized fractional integral

Ilknur Yesilce

doi:10.1186/s13660-019-2150-3

Abstract

Recently, fractional calculus has become a very popular and important area. Specially, fractional integral inequalities have been studied by different authors. In this article, we give new Hermite–Hadamard type inequalities for mathbb{B}-convex functions via Riemann–Liouville and Hadamard fractional integrals. Also, we show that the inequalities involve the fractional integrals of a function with respect to the function g which are the more general form of these obtained Hermite–Hadamard inequalities.

Highlights

The idea of fractional calculus was suggested by Leibnitz via a letter to L’Hospital
For integral inequalities, which is the topic of this work, fractional integrals have been used, familiar significant inequalities can be generalized using this type of integrals
We prove Hermite–Hadamard inequalities for B-convex functions via fractional integrals of a function with respect to the function g

Summary

Introduction

The idea of fractional calculus was suggested by Leibnitz via a letter to L’Hospital. For B-convex functions, Riemann–Liouville fractional Hermite–Hadamard inequality was studied in [36]. The most general form of Hermite–Hadamard inequality for B-convex functions is obtained. We prove Hermite–Hadamard inequalities for B-convex functions via fractional integrals of a function with respect to the function g.

Results

Conclusion