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Open Journal of Mathematical Sciences (OMS)

ISSN: 2523-0212 (Online) 2616-4906 (Print)
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  • Research article

On some properties and integral inequalities for modified \((p,h)\)-convex Stochastic processes

Amad Adrees1, Waqar Afzal2,3, Khurram Shabbir1, Nahed Mustafa Dahshan4, Amani Elseid Abuzeid5, Ranya A. Tahir4, Muhammad Tariq6, Hijaz Ahmad7,8
1Department of Mathematics, Government College University Lahore (GCUL), Lahore 54000, Pakistan
2Center for Theoretical Physics, Khazar University, 41 Mehseti Str., Baku, AZ1096, Azerbaijan
3Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, 54600 Lahore, Pakistan
4Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
5Department of Mathematics, University College of Aldayer, Saudi Arabia
6Mathematics Research Center, Near East University, Near East Boulevard, Nicosia, Mersin, 99138, Turkey
7Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea
8Irfan Suat Günsel Operational Research Institute, Near East University, Nicosia/TRNC, Mersin 10, 99138, Turkey
Copyright © Amad Adrees, Waqar Afzal, Khurram Shabbir, Nahed Mustafa Dahshan, Amani Elseid Abuzeid, Ranya A. Tahir, Muhammad Tariq, Hijaz Ahmad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • Received: 22/02/2026
  • Revised: 01/04/2026
  • Accepted: 05/04/2026
  • Published: 06/05/2026

Abstract

In this paper, we introduce and study the class of modified \((p, h)\)-convex stochastic processes, which unifies and extends several existing notions of convexity in the stochastic setting. We establish fundamental arithmetic properties of this class and derive Hermite–Hadamard-type inequalities using classical and fractional Katugampola-type operators. We also investigated Ostrowski-type and Jensen-type inequalities in a simple and unified framework. Our results generalize and unify many existing results in the literature, providing a comprehensive framework for the study of convex stochastic processes.

Keywords: Hermite–Hadamard inequality, Ostrowski inequality, Jensen inequality, stochastic processes, generalized convexity