Some integral inequalities for harmonical $ cr $-$ h $-Godunova-Levin stochastic processes

Waqar Afzal; Sayed M. Eldin; Waqas Nazeer; Ahmed M. Galal; Waqar Afzal; Sayed M. Eldin; Waqas Nazeer; Ahmed M. Galal

doi:10.3934/math.2023683

AIMS Mathematics

2023, Volume 8, Issue 6: 13473-13491. doi: 10.3934/math.2023683

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Some integral inequalities for harmonical $ cr $-$ h $-Godunova-Levin stochastic processes

1.
Department of Mathemtics, Government College University Lahore (GCUL), Lahore 54000, Pakistan
2.
Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan
3.
Center of Research, Faculty of Engineering, Future University in Egypt New Cairo 11835, Egypt
4.
Department of Mechanical Engineering, College of Engineering in Wadi Alddawasir, Prince Sattam bin Abdulaziz University, Saudi Arabia
5.
Production Engineering and Mechanical Design Department, Faculty of Engineering, Mansoura University, P.O. Box 35516, Mansoura, Egypt

Received: 19 October 2022 Revised: 24 December 2022 Accepted: 29 December 2022 Published: 06 April 2023
MSC : 39B62, 52B55, 94B75

An important part of optimization is the consideration of convex and non-convex functions. Furthermore, there is no denying the connection between the ideas of convexity and stochastic processes. Stochastic processes, often known as random processes, are groups of variables created at random and supported by mathematical indicators. Our study introduces a novel stochastic process for center-radius (cr) order based on harmonic h-Godunova-Levin ($ \mathcal{GL} $) in the setting of interval-valued functions ($ \mathcal{IVFS} $). With some interesting examples, we establish some variants of Hermite-Hadamard ($ \mathcal{H.H} $) types inequalities for generalized interval-valued harmonic cr-h-Godunova-Levin stochastic processes.
- Jensen inequality,
- Hermite-Hadamard inequality,
- Godunova-Levin function,
- cr-order relation,
- stochastic h-convex
Citation: Waqar Afzal, Sayed M. Eldin, Waqas Nazeer, Ahmed M. Galal. Some integral inequalities for harmonical $ cr $-$ h $-Godunova-Levin stochastic processes[J]. AIMS Mathematics, 2023, 8(6): 13473-13491. doi: 10.3934/math.2023683

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Abstract

An important part of optimization is the consideration of convex and non-convex functions. Furthermore, there is no denying the connection between the ideas of convexity and stochastic processes. Stochastic processes, often known as random processes, are groups of variables created at random and supported by mathematical indicators. Our study introduces a novel stochastic process for center-radius (cr) order based on harmonic h-Godunova-Levin ($ \mathcal{GL} $) in the setting of interval-valued functions ($ \mathcal{IVFS} $). With some interesting examples, we establish some variants of Hermite-Hadamard ($ \mathcal{H.H} $) types inequalities for generalized interval-valued harmonic cr-h-Godunova-Levin stochastic processes.

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