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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Evidence of a conspiracy among fixed point theorems

Author: Ira Rosenholtz
Journal: Proc. Amer. Math. Soc. 53 (1975), 213-218
MSC: Primary 54H25
MathSciNet review: 0400201
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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 [Enhancements On Off] (What's this?)

  • [1] Michael Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc. 12 (1961), 7-10. MR 22 #11375. MR 0120625 (22:11375)
  • [2] -, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74-79. MR 24 #A2936. MR 0133102 (24:A2936)
  • [3] Ira Rosenholtz, Local expansions, derivatives, and fixed points, Fund. Math. (to appear). MR 0410719 (53:14465)

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Keywords: Fixed points, Banach contraction theorem, remetrization, contractions, local contractions, contractive maps, locally contractive maps, local expansions, locally expansive maps
Article copyright: © Copyright 1975 American Mathematical Society

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