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A fixed point theorem for locally nonexpansive mappings in normed spaces


Author: C. Waters
Journal: Proc. Amer. Math. Soc. 97 (1986), 695-699
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1986-0845990-0
MathSciNet review: 845990
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Abstract: It is shown that global conditions in a recent result of W. A. Kirk can be replaced with the corresponding local conditions in case the domain is connected. Also a remark is made about the proof of the theorem referenced.


References [Enhancements On Off] (What's this?)

  • [1] H. Freundenthal and W. Hurewicz, Duhnungen, Verkurzungen, Isometrien, Fund. Math. 26 (1936), 120-122.
  • [2] W. A. Kirk, Remarks on fixed points and boundaries, Proc. Amer. Math. Soc. 87 (1983), 62-64. MR 677232 (84c:47059)
  • [3] I. Rosenholtz, Evidence of a conspiracy among fixed point theorems, Proc. Amer. Math. Soc. 52 (1975), 312-318. MR 0400201 (53:4036)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0845990-0
Keywords: Locally contractive, locally nonexpansive, chainable
Article copyright: © Copyright 1986 American Mathematical Society

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