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Generic Well-Posedness of Fixed Point Problems

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Abstract

We study generic well-posedness of fixed point problems for certain complete metric spaces of mappings. We first establish the equivalence of this generic well-posedness to certain assumptions which are not difficult to verify. Then, we show that several known results in the literature can be deduced from these equivalences.

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Acknowledgements

The first author was partially supported by the Israel Science Foundation (Grant No. 389/12), by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund.

Both authors are grateful to an anonymous referee for several helpful suggestions.

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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

Authors
  1. Simeon Reich
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  2. Alexander J. Zaslavski
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Correspondence to Simeon Reich.

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Dedicated to Professor Michel Théra on his 70th birthday.

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Reich, S., Zaslavski, A.J. Generic Well-Posedness of Fixed Point Problems. Vietnam J. Math. 46, 5–13 (2018). https://doi.org/10.1007/s10013-017-0251-1

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  • DOI: https://doi.org/10.1007/s10013-017-0251-1

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