On the Uniqueness of Best Non-decreasing Approximation in Orlicz Spaces

2025/12/10 by Ana Benavente, Benavente, Ana, Juan Costa Ponce +3
Mathematics · #Approximation Theory and Sequence Spaces #Advanced Banach Space Theory #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.2512.09210

Abstract

Given an approximately continuous function f in an Orlicz space L^Φ([a,b]), for a suitable class of convex functions Φ, we employ a characterization of the best monotone approximation set to establish its continuity, which in turn yields the uniqueness property for the best monotone approximation in L^Φ([a,b]).

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