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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.

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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