Integral inequalities for s-convex functions via generalized conformable fractional integral operators

Artion Kashuri,Sajid Iqbal,Rozana Liko,Muhammad Samraiz,Wei Gao

doi:10.1186/s13662-020-02671-4

Abstract

We introduce new operators, the so-called left and right generalized conformable fractional integral operators. By using these operators we establish new Hermite–Hadamard inequalities for s-convex functions and products of two s-convex functions in the second sense. Also, we obtain two interesting identities for a differentiable function involving a generalized conformable fractional integral operator. By applying these identities we give Hermite–Hadamard and midpoint-type integral inequalities for s-convex functions. Different special cases have been identified and some known results are recovered from our general results. These results may motivate further research in different areas of pure and applied sciences.

Highlights

The theory of inequalities is known to play an important role in almost all areas of pure and applied sciences
4 Conclusion Trapezium-type integral inequalities for functions of divers natures are useful in numerical computations
Using the generalized conformable fractional integral operators defined in our paper, the interested reader can obtain in a similar way new results for different operators, such as k-Riemann–Liouville fractional integral, Katugampola fractional integrals, the conformable fractional integral, (p, q)-quantum calculus, Hadamard fractional integrals, and so on

Summary

Introduction

The theory of inequalities is known to play an important role in almost all areas of pure and applied sciences. . Set et al [30] obtained a new generalized class of Hermite–Hadamard-type inequalities for s-convex functions by applying conformable fractional integrals.

Results

Conclusion