Lara, T., Matkowski, J., Merentes, N., Quintero, R. and Wróbel, M. (2017) A Generalization of M-Convexity and a Sandwich Theorem. Annales Mathematicae Silesianae, 31, 107-126.
https://doi.org/10.1515/amsil-2017-0003

has been cited by the following article:

• 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.