Some New Refinements of Trapezium-Type Integral Inequalities in Connection with Generalized Fractional Integrals

Abstract

The main objective of this article is to introduce a new notion of convexity, i.e., modified exponential type convex function, and establish related fractional inequalities. To strengthen the argument of the paper, we introduce two new lemmas as auxiliary results and discuss some algebraic properties of the proposed notion. Considering a generalized fractional integral operator and differentiable mappings, whose initial absolute derivative at a given power is a modified exponential type convex, various improvements of the Hermite–Hadamard inequality are presented. Thanks to the main results, some generalizations about the earlier findings in the literature are recovered.