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Proceedings of the American Mathematical Society

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A fixed point theorem revisited

Authors: Alberta Bollenbacher and T. L. Hicks
Journal: Proc. Amer. Math. Soc. 102 (1988), 898-900
MSC: Primary 54H25
MathSciNet review: 934863
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Abstract: A version of a theorem commonly referred to as Caristi's Theorem is given. It has an elementary constructive proof and it includes many generalizations of Banach's fixed point theorem. Several examples illustrate the diversity that can occur.

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

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  • [2] J. Eisenfeld and V. Lakshmikantham, Fixed point theorems on closed sets through abstract cones, Appl. Math. Comput. 3 (1977), 155-167. MR 444873 (81i:47057)
  • [3] T. L. Hicks and B. E. Rhoades, A Banach type fixed point theorem, Math. Japon. 24 (1979), 327-330. MR 550217 (80i:54055)
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Keywords: Fixed point theorem, Caristi's theorem, Banach's theorem
Article copyright: © Copyright 1988 American Mathematical Society

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