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

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.

Keywords

• Hermite–Hadamard
• Jensen–Mercer inclusions
• interval-valued functions
• mean-square fractional integral
• γ-convexity
• interval-valued stochastic γ-convexity with center-radius order relation