TITLE:
A Sandwich Theorem for m-Convex Stochastic Processes
AUTHORS:
Ángel Padilla, Ronald Ramírez, Maira Valera-López
KEYWORDS:
m-Convex Stochastic Processes, Hermite-Hadamard Inequality, Sandwich Theorem, Hyer-Ulam’s Stability
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.15 No.7,
July
11,
2025
ABSTRACT: In this paper, we present some properties of m-convex stochastic processes. The most important results are: a generalization of the sandwich theorem and a result on Hyers-Ulam stability, given for m-convex functions. The first result allows us to bound an m-convex stochastic process by two convex stochastic processes, and the second allows us to approximate controlled perturbations of an m-convex stochastic process by an m-convex function. As a consequence of these two results, we obtain a Hermite-Hadamard type inequality for m-convex stochastic processes.