A Generalized Convexity and Inequalities Involving the Unified Mittag-Leffler Function

This article aims to obtain inequalities containing the unified Mittag-Leffler function which give bounds of integral operators for a generalized convexity. These findings provide generalizations and refinements of many inequalities. By setting values of monotone functions, it is possible to reproduce results for classical convexities. The Hadamard-type inequalities for several classes related to convex functions are identified in remarks, and some of them are also presented in last section.