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Fractional Hermite–Hadamard–Mercer-Type Inequalities for Interval-Valued Convex Stochastic Processes with Center-Radius Order and Their Related Applications in Entropy and Information Theory

Authors :
Ahsan Fareed Shah
Serap Özcan
Miguel Vivas-Cortez
Muhammad Shoaib Saleem
Artion Kashuri
Source :
Fractal and Fractional, Vol 8, Iss 7, p 408 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

Abstract

We propose a new definition of the γ-convex stochastic processes (CSP) using center and radius (CR) order with the notion of interval valued functions (C.RI.V). By utilizing this definition and Mean-Square Fractional Integrals, we generalize fractional Hermite–Hadamard–Mercer-type inclusions for generalized C.RI.V versions of convex, tgs-convex, P-convex, exponential-type convex, Godunova–Levin convex, s-convex, Godunova–Levin s-convex, h-convex, n-polynomial convex, and fractional n-polynomial (CSP). Also, our work uses interesting examples of C.RI.V(CSP) with Python-programmed graphs to validate our findings using an extension of Mercer’s inclusions with applications related to entropy and information theory.

Details

Language :
English
ISSN :
25043110
Volume :
8
Issue :
7
Database :
Directory of Open Access Journals
Journal :
Fractal and Fractional
Publication Type :
Academic Journal
Accession number :
edsdoj.32b5329fd0714548b6faf44fddf845c0
Document Type :
article
Full Text :
https://doi.org/10.3390/fractalfract8070408