Generalization of integral inequalities via new class strongly convex functions

Abstract

The main objective of this study is to extend the concept of strong
convexity by introducing a new class of modified $(h,m)$-strongly convex
functions. Using this new concept, we generalize the Hermite-Hadamard
inequalities through the Caputo-Fabrizio integral operator. To achieve this,
we establish a new identity for a twice-differentiable function within the
framework of the Caputo-Fabrizio fractional integral operator. Using this
identity as an auxiliary result, we present a new version of the midpoint
inequality, utilizing well-known inequalities such as H\"{o}lder's and the
power mean inequality.