Local contractions in metric spaces
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- by Thakyin Hu and W. A. Kirk PDF
- Proc. Amer. Math. Soc. 68 (1978), 121-124 Request permission
Abstract:
It is shown that a theorem of E. Rakotch for locally contractive mappings can be deduced from Banach’s contraction mapping theorem, and a counterexample to an assertion of R. D. Holmes concerning local radial contractions is given.References
- Leonard M. Blumenthal, Theory and applications of distance geometry, Oxford, at the Clarendon Press, 1953. MR 0054981
- R. D. Holmes, Fixed point for local radial contractions, Fixed point theory and its applications (Proc. Sem., Dalhousie Univ., Halifax, N.S., 1975) Academic Press, New York, 1976, pp. 79–89. MR 0448327
- E. Rakotch, A note on $\alpha$-locally contractive mappings, Bull. Res. Council Israel Sect. F 10F (1962), 188–191 (1962). MR 146799
- Willi Rinow, Die innere Geometrie der metrischen Räume, Die Grundlehren der mathematischen Wissenschaften, Band 105, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0123969
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 121-124
- MSC: Primary 54E40; Secondary 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1978-0464180-2
- MathSciNet review: 0464180