New Jensen-type integral inequalities via modified $(h,m)$-convexity and their applications

Abstract

This article presents new developments and applications of Jensen's inequality. We explore various variations of Jensen's inequality related to modified $(h,m)$-convex functions. The obtained results extend the applicability of the inequality to a broader class of functions and contexts. In addition to the fact that the results presented in the article provide additional results available in the literature, we also give examples of their application.