Generic Aspects of Metric Fixed Point Theory

Simeon Reich () and Alexander J. Zaslavski ()
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Simeon Reich: The Technion-Israel Institute of Technology, Department of Mathematics
Alexander J. Zaslavski: The Technion-Israel Institute of Technology, Department of Mathematics

Chapter Chapter 16 in Handbook of Metric Fixed Point Theory, 2001, pp 557-575 from Springer

Abstract: Abstract Let X be a complete metric space. According to Baire’s theorem, the intersection of every countable collection of open dense subsets of X is dense in X. This rather simple, yet powerful result has found many applications. In particular, given a property which elements of X may have, it is of interest to determine whether this property is generic, that is, whether the set of elements which do enjoy this property contains a countable intersection of open dense sets. Such an approach, when a certain property is investigated for the whole space X and not just for a single point in X, has already been successfully applied in many areas of Analysis. We mention, for instance, the theory of dynamical systems [12, 18, 24, 35, 33, 52], optimization [22, 44], variational analysis [2, 9], [20, 211, the calculus of variations [4, 14, 55] and optimal control [56, 57].

Keywords: Nonexpansive Mapping; Hyperbolic Space; Weak Topology; Nonempty Closed Convex Subset; Strong Topology (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-94-017-1748-9_16

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