@article{Afzal2023, 
author = {Waqar Afzal and Thongchai Botmart},
title = {Some novel estimates of Jensen and Hermite-Hadamard inequalities for h-Godunova-Levin stochastic processes},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {7277-7291},
keywords = {Jensen inequality, Hermite-Hadamard inequality, interval valued functions, Godunova-Levin stochastic process},
url = {https://www.sciopen.com/article/10.3934/math.2023366},
doi = {10.3934/math.2023366},
abstract = {It is undeniable that convex and non-convex functions play an important role in optimization. As a result of its behavior, convexity also plays a significant role in discussing inequalities. It is clear that convexity and stochastic processes are intertwined. The stochastic process is a mathematical model that describes how systems or phenomena fluctuate randomly. Probability theory generally says that the convex function applied to the expected value of a random variable is bounded above by the expected value of the random variable's convex function. Furthermore, the deep connection between convex inequalities and stochastic processes offers a whole new perspective on the study of inequality. Although Godunova-Levin functions are well known in convex theory, their properties enable us to determine inequality terms with greater accuracy than those obtained from convex functions. In this paper, we established a more refined form of Hermite-Hadamard and Jensen type inequalities for generalized interval-valued h-Godunova-Levin stochastic processes. In addition, we provide some examples to demonstrate the validity of our main findings.}
}