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Handbook of Metric Fixed Point Theory pp 557–575Cite as

Generic Aspects of Metric Fixed Point Theory

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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].

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Authors and Affiliations

  1. Department of Mathematics, The Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Simeon Reich & Alexander J. Zaslavski

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  1. Simeon Reich
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  2. Alexander J. Zaslavski
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Editors and Affiliations

  1. Department of Mathematics, The University of Iowa, Iowa City, IA, USA

    William A. Kirk

  2. School of Mathematical and Physical Sciences, The University of Newcastle, Newcastle, Australia

    Brailey Sims

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Reich, S., Zaslavski, A.J. (2001). Generic Aspects of Metric Fixed Point Theory. In: Kirk, W.A., Sims, B. (eds) Handbook of Metric Fixed Point Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1748-9_16

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  • DOI: https://doi.org/10.1007/978-94-017-1748-9_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5733-4

  • Online ISBN: 978-94-017-1748-9

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