Mathematics and Statistics Vol. 12(5), pp. 501 - 513
DOI: 10.13189/ms.2024.120512
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Extending Godunova-Levin Interval-Valued Functions to Stochastic Processes: New Hermite-Hadamard and Jensen-Type Inequalities

Oualid Rholam ¹, Yassine Laarichi ^2,*, Mariem Elkaf ³, Amal Aloui ^4
1 National School of Applied Sciences, University Ibn Tofail, Kenitra, Morocco
² University Ibn Tofail, Kenitra, Morocco
³ Royal Naval School, Casablanca, Morocco
⁴ Laboratory of Analysis, Geometry and Applications-LAGA, Department of Mathematics, Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco

ABSTRACT

This paper attempts to broaden the scope of the interval-valued functions by proposing the concept of Godunova-Levin interval-valued functions as stochastic processes. We present a novel framework for interval-valued harmonical (h1, h2)-Godunova-Levin stochastic processes. This approach seeks to address the inherent uncertainty and variability in real-world phenomena by establishing a solid mathematical foundation for interval-valued functions in stochastic settings. The fundamental goal of this study is to obtain fresh estimates for interval Hermite-Hadamard and Jensen-type inequalities in the setting of these stochastic processes. We obtain important results using sophisticated stochastic analysis and interval arithmetic approaches, which not only generalize existing inequalities but also provide a deeper understanding of the behavior of interval-valued functions under stochastic effects. The findings of this study have the potential to improve the applicability of interval-valued functions in a variety of stochastic scenarios, including financial modeling, engineering, and decision-making under uncertainty. Furthermore, the theoretical advances discussed here contribute to the larger subject of stochastic processes, bringing up new opportunities for research and application. However, the assumptions underpinning interval-valued functions and stochastic processes may limit the applicability of the presented approaches. Future study could investigate the relaxing of these assumptions and the application of the suggested framework to more complex stochastic systems.

KEYWORDS
Hermite-Hadamard Inequalities, Godunova-Levin Interval-valued Stochastic Process, Harmonical H-convex Stochastic Process

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Oualid Rholam , Yassine Laarichi , Mariem Elkaf , Amal Aloui , "Extending Godunova-Levin Interval-Valued Functions to Stochastic Processes: New Hermite-Hadamard and Jensen-Type Inequalities," Mathematics and Statistics, Vol. 12, No. 5, pp. 501 - 513, 2024. DOI: 10.13189/ms.2024.120512.

(b). APA Format:
Oualid Rholam , Yassine Laarichi , Mariem Elkaf , Amal Aloui (2024). Extending Godunova-Levin Interval-Valued Functions to Stochastic Processes: New Hermite-Hadamard and Jensen-Type Inequalities. Mathematics and Statistics, 12(5), 501 - 513. DOI: 10.13189/ms.2024.120512.