Inequalities of the Hermite-Hadamard Type for Stochastic Processes with Convexity-Preserving Properties

Abstract

In this study, we delve into the exploration of Hermite-Hadamard type inequalities specifically tailored for stochastic processes with convexity-preserving properties. The primary research objective is to examine the convexity characteristics of the derivatives of these processes, establishing new bounds and providing deeper insights into their behavior. Through a systematic investigation, we aim to expand upon the classical Hermite-Hadamard inequality by incorporating these unique stochastic processes. By employing a recently introduced fractional integral operator, the analysis introduces a novel dimension to the study of mathematical inequalities in the context of stochastic processes.