Hermite-Hadamard-Fejèr type inequalities for s-convex functions in the second sense via Riemann-Liouville fractional integral

Abstract

The convex function is one of the topics in mathematics that is closely related to the theory of inequality. Furthermore, the definition of convex function has an extension, which is the first and second kind of s-convex function, for fixed s ∈ (0,1. Convex function has a relation to the Hermite-Hadamard-Fejèr inequality, which is an integral inequality involving a convex function. Further development of these inequalities involves the s-convex function and through the concept of fractional integral. In this study, we discuss the Hermite-Hadamard-Fejèr type inequality that applies to the second kind of s-convex function via the Riemann-Liouville fractional integral. From these results, the relationship between these inequalities with the same type of inequality for convex function, are obtained.