A fixed point theorem revisited

Authors:
Alberta Bollenbacher and T. L. Hicks

Journal:
Proc. Amer. Math. Soc. **102** (1988), 898-900

MSC:
Primary 54H25

DOI:
https://doi.org/10.1090/S0002-9939-1988-0934863-2

MathSciNet review:
934863

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**J. Caristi,*Fixed point theorems for mappings satisfying inwardness conditions*, Trans. Amer. Math. Soc.**215**(1976), 241-251. MR**0394329 (52:15132)****[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)****[4]**B. E. Rhoades,*Contractive definitions revisited*, Topological Methods in Nonlinear Functional Analysis, Contemp. Math., vol. 21, Amer. Math. Soc., Providence, R. I., 1983, pp. 190-205. MR**729516 (85d:47060)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0934863-2

Keywords:
Fixed point theorem,
Caristi's theorem,
Banach's theorem

Article copyright:
© Copyright 1988
American Mathematical Society