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Proceedings of the American Mathematical Society

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A new proof of Caristi's fixed point theorem


Author: Jerrold Siegel
Journal: Proc. Amer. Math. Soc. 66 (1977), 54-56
MSC: Primary 54H25
DOI: https://doi.org/10.1090/S0002-9939-1977-0458403-2
MathSciNet review: 0458403
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Abstract | References | Similar Articles | Additional Information

Abstract: An elementary proof of Caristi's generalization of the contraction theorem is presented.


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

  • [1] A. Brøndsted, On a lemma of Bishop and Phelps, Pacific J. Math. 55 (1974), 335-341. MR 0380343 (52:1243)
  • [2] F. E. Browder, On a theorem of Caristi and Kirk, Proc. Seminar on Fixed Point Theory and its Applications, Dalhousie University, June 1975 (to appear). MR 0461474 (57:1459)
  • [3] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251. MR 0394329 (52:15132)
  • [4] I. Ekeland, Sur les problèmes variationnels, C. R. Acad. Sci. Paris 275 (1972), 1057-1059. MR 0310670 (46:9768)
  • [5] C. S. Wong, On a fixed point theorem of contractive type, Proc. Amer. Math. Soc. 57 (1976), 283-284. MR 0407826 (53:11596)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0458403-2
Keywords: Contraction theorem, fixed point theorem, complete metric space
Article copyright: © Copyright 1977 American Mathematical Society

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