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A Stone-Weierstrass approximation theorem for monotone functions

2025/12/03 by E. Minguzzi, Minguzzi, Ettore
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #FOS: Physical sciences #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #General Topology (math.GN) #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2512.03633

openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28

Abstract

We present an approximation theorem for continuous non-decreasing functions on compact preordered spaces, leading to an algebraic characterization of their corresponding function spaces. As an application, we prove that the family of positive non-decreasing rational functions with non-negative coefficients can uniformly approximate all continuous non-decreasing functions on compact intervals. An explicit approximation formula of this type is provided.

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