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Peer-reviewedCC BYInternational Journal of Analysis and Applications

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

  • Amad Adrees1
  • Waqar Afzal2,3
  • Mehreen Shehzadi Khan4
  • Hafeez Sultana4
  • Omniat Omer Yousif Karrar4
  • Leema Aliyarukunju4
  • Jorge E. Macías-Díaz5,6
  • Alejandro Román-Loera7
  • Daniel Breaz8
  • Luminiţa-Ioana Cotîrlă9
9 affiliations
  1. 1Department of Mathematics , Government College University Lahore (GCUL) , Lahore 54000 , Pakistan
  2. 2Abdus Salam School of Mathematical Sciences , GC University , Lahore , Pakistan
  3. 3Center for Theoretical Physics , Khazar University , 41 Mehseti Str. , Baku , AZ1096 , Azerbaijan
  4. 4Department of Mathematics , Faculty of Science , Jazan University , Jazan 45142 , Saudi Arabia
  5. 5Department of Mathematics and Didactics of Mathematics , Tallinn University , 10120 Tallinn , Estonia
  6. 6Department of Mathematics and Physics , Autonomous University of Aguascalientes , Aguascalientes 20100 , Mexico
  7. 7Department of Electronics , Autonomous University of Aguascalientes , Ave. Universidad 940 , Ciudad Universitaria , Aguascalientes 20100 , Mexico
  8. 8Department of Mathematics , "1 Decembrie 1918 " University of Alba Iulia , 510009 Alba Iulia , Romania
  9. 9Department of Mathematics , Technical University of Cluj-Napoca , 400114 Cluj-Napoca , Romania
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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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Cite

BibTeXRIS
BibTeX
@article{adrees2026novel,
  title = {{Novel Unified Variants, Properties, and Applications of Ostrowski, Jensen, and Hermite–Hadamard Inequalities for Generalized (η, p, h)-Convex Stochastic Processes}},
  author = {Amad Adrees and Waqar Afzal and Mehreen Shehzadi Khan and Hafeez Sultana and Omniat Omer Yousif Karrar and Leema Aliyarukunju and Jorge E. Macías-Díaz and Alejandro Román-Loera and Daniel Breaz and Luminiţa-Ioana Cotîrlă},
  journal = {International Journal of Analysis and Applications},
  year = {2026},
  month = may,
  doi = {10.28924/2291-8639-24-2026-164},
  url = {https://doi.org/10.28924/2291-8639-24-2026-164},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Novel Unified Variants, Properties, and Applications of Ostrowski, Jensen, and Hermite–Hadamard Inequalities for Generalized (η, p, h)-Convex Stochastic Processes
AU  - Amad Adrees
AU  - Waqar Afzal
AU  - Mehreen Shehzadi Khan
AU  - Hafeez Sultana
AU  - Omniat Omer Yousif Karrar
AU  - Leema Aliyarukunju
AU  - Jorge E. Macías-Díaz
AU  - Alejandro Román-Loera
AU  - Daniel Breaz
AU  - Luminiţa-Ioana Cotîrlă
PY  - 2026
DA  - 2026/05/29
JO  - International Journal of Analysis and Applications
DO  - 10.28924/2291-8639-24-2026-164
UR  - https://doi.org/10.28924/2291-8639-24-2026-164
AB  - 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.
SN  - 2291-8639
ER  -