On Chebyshev centers in Banach spaces

2025/08/14 by Syamantak Das, Das, Syamantak, Tanmoy Paul +1
Mathematics · #Advanced Banach Space Theory #Fixed Point Theorems Analysis #Nonlinear Differential Equations Analysis

paper · doi:10.48550/arxiv.2508.11087

Abstract

In this note, we observe that X∈ (GC) if X admits Chebyshev center for any finite set in it. This answers the problem raised by Veselý, addressed in [\em Generalized centers of finite sets in Banach spaces, Acta Math. Univ. Comenian. (N.S.) \bf 66(1) (1997), 83--115]. We extend our observation towards the fact that the property (GC) is not a 3-space property.

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