Novel Unified Variants, Properties, and Applications of Ostrowski, Jensen, and Hermite–Hadamard Inequalities for Generalized (η, p, h)-Convex Stochastic Processes

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DOI: https://doi.org/10.28924/2291-8639-24-2026-164
Published: May 29, 2026
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Amad Adrees, Waqar Afzal, Mehreen Shehzadi Khan, Hafeez Sultana, Omniat Omer Yousif Karrar, Leema Aliyarukunju, Jorge E. Macías-Díaz, Alejandro Román-Loera, Daniel Breaz, Luminiţa-Ioana Cotîrlă, Novel Unified Variants, Properties, and Applications of Ostrowski, Jensen, and Hermite–Hadamard Inequalities for Generalized (η, p, h)-Convex Stochastic Processes, Int. J. Anal. Appl., 24 (2026), 164.

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Amad Adrees, Waqar Afzal, Mehreen Shehzadi Khan, Hafeez Sultana, Omniat Omer Yousif Karrar, Leema Aliyarukunju, Jorge E. Macías-Díaz, Alejandro Román-Loera, Daniel Breaz, Luminiţa-Ioana Cotîrlă

Abstract

Stochastic processes play a crucial role in functional analysis and the study of inequalities under uncertainty, with Wiener processes providing a fundamental model for random perturbations. In this work, we introduce a new class of generalized (η, p, h)-convex stochastic processes, which unifies and extends several existing notions of convexity in the stochastic setting. We investigate essential properties of this class and derive novel Ostrowski-, Jensen-, and Hermite–Hadamard-type inequalities. The validity and effectiveness of the obtained results are illustrated through non-trivial examples and graphical comparisons highlighting the impact of Wiener processes relative to deterministic components.

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