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.

Automated summary

This article aims to derive inequalities involving the unified Mittag-Leffler function, providing bounds for integral operators in generalized convexity. These findings extend and refine many existing inequalities. By assigning values to monotone functions, classical convexity results can be reproduced. Various Hadamard-type inequalities for classes related to convex functions are identified in remarks and some are also presented in the last section.