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Fixed points and invariant approximation in random normed spaces. (English) Zbl 1212.47038

Summary: The aim of this paper is to provide necessary conditions for the existence of fixed points of nonexpansive mappings on a nonconvex domain of a random normed space. As an application, related results on invariant approximation are also derived.

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
41A50 Best approximation, Chebyshev systems
47H40 Random nonlinear operators
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