Classical Theory of Nonexpansive Mappings

Kazimierz Goebel () and W. A. Kirk ()
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Kazimierz Goebel: Maria Curie-Skłodowska University
W. A. Kirk: The University of Iowa, Department of Mathematics

Chapter Chapter 3 in Handbook of Metric Fixed Point Theory, 2001, pp 49-91 from Springer

Abstract: Abstract Mappings which are defined on metric spaces and which do not increase distances between pairs of points and their images are called nonexpansive. Thus an abstract metric space is all that is needed to define the concept. At the same time, the more interesting results seem to require some notion of topology; more specifically a topology which assures that closed metric balls are compact. This is not a serious limitation, however, because many spaces which arise naturally in functional analysis possess such topologies; most notably the weak and weak* topologies in Banach spaces.

Keywords: Banach Space; Convex Subset; Nonexpansive Mapping; Convex Space; Convexity Structure (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-94-017-1748-9_3

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