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Bakula, M.K., Pecaric, J. and Ribicic, M. (2006) Companion Inequalities to Jensens Inequality for M-Convex and (a, m)-Convex Functions. Journal of Inequalities in Pure and Applied Mathematics, 7, 26-35.

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.