Evidence of a conspiracy among fixed point theorems
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- by Ira Rosenholtz PDF
- Proc. Amer. Math. Soc. 53 (1975), 213-218 Request permission
Abstract:
Some generalizations of the Banach contraction theorem replace the global hypothesis that the function be a contraction with various local hypotheses. In this paper, we examine a few of these, and show that, in fact, the functions actually satisfied the global hypothesis after a suitable change of metric. Finally, the techniques developed are applied to prove a new fixed point theorem for locally expansive maps.References
- Michael Edelstein, An extension of Banach’s contraction principle, Proc. Amer. Math. Soc. 12 (1961), 7–10. MR 120625, DOI 10.1090/S0002-9939-1961-0120625-6
- M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74–79. MR 133102, DOI 10.1112/jlms/s1-37.1.74
- Ira Rosenholtz, Local expansions, derivatives, and fixed points, Fund. Math. 91 (1976), no. 1, 1–4. MR 410719, DOI 10.4064/fm-91-1-1-4
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 213-218
- MSC: Primary 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1975-0400201-8
- MathSciNet review: 0400201