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A Sandwich Theorem for m -Convex Stochastic Processes
Department of Mathematics, Faculty of Sciences, Universidad Metropolitana, Caracas, Venezuela
Department of Mathematics, Faculty of Sciences, Universidad Central de Venezuela, Caracas, Venezuela
Department of Mathematics, Faculty of Sciences, Universidad Central de Venezuela, Caracas, Venezuela
- 1 Department of Mathematics, Faculty of Sciences, Universidad Metropolitana, Caracas, Venezuela
- 2 Department of Mathematics, Faculty of Sciences, Universidad Central de Venezuela, Caracas, Venezuela
- 3 Department of Mathematics, Faculty of Sciences, Universidad Central de Venezuela, Caracas, Venezuela
Advances in Pure Mathematics·Volume 15 (2025)·Pages 459–471·Published 11 July 2025·DOI10.4236/apm.2025.157021
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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.
Keywordsm -Convex Stochastic ProcessesHermite-Hadamard InequalitySandwich TheoremHyer-Ulam’s Stability
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