Volume 2 - Issue 2, March - April 2026

In this paper, we explore a set of generalized concepts associated with convex stochastic processes and their structural properties. Stochastic processes are among the most fundamental components of probability theory, providing a mathematical framework for modeling systems that evolve randomly over time. Recognizing the importance of convexity in analyzing such processes, we extend the classical notion of convexity and introduce the concept of a generalized modified pH-convex stochastic process. This newly developed framework enables a broader class of stochastic functions to be examined in various integral and inequality settings. Furthermore, we investigate the behaviour of these generalized processes with respect to wellestablished inequalities, specifically, those of Hermite, Hadamard, Jensen, and Ostrowski. By establishing these generalized inequalities, our results not only unify several existing findings but also offer new analytical tools that may lead to deeper insights in stochastic analysis, optimization, and applied probability.

Amad Adrees, Muhammad Amad Sarwar, Abdul Khaliq, Sultana Rinke, "Jensen, Hermite-Hadamard, and Ostrowski Type Inequalities for a Generalized Class of Convex Stochastic Functions" International Journal of Advanced Multidisciplinary Research and Educational Development, V2(2): Page(141-164) Mar-Apr 2026. ISSN: 3107-6513. www.ijamred.com. Published by Scientific and Academic Research Publishing.