On a fixed point theorem of contractive type

Author:
Chi Song Wong

Journal:
Proc. Amer. Math. Soc. **57** (1976), 283-284

MSC:
Primary 54H25; Secondary 47H10

DOI:
https://doi.org/10.1090/S0002-9939-1976-0407826-5

MathSciNet review:
0407826

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Abstract | References | Similar Articles | Additional Information

Abstract: A refinement of the proof of a recent fixed point theorem of Caristi is obtained.

**[1]**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)****[2]**A. Brønsted,*On a lemma of Bishop and Phelps*, Pacific J. Math.**55**(1974), 335-341. MR**0380343 (52:1243)****[3]**J. Caristi,*Fixed point theorems for mappings satisfying inwardness conditions*, Trans. Amer. Math. Soc.**215**(1976), 241-251. MR**0394329 (52:15132)****[4]**J. Caristi and W. A. Kirk,*Geometric fixed point theory and inwardness conditions*, Proc. Conf. on Geometry of Metric and Linear Spaces, Michigan State University, 1974 (to appear). MR**0399968 (53:3806)****[5]**I. Ekeland,*Sur les problémes variationnels*, C. R. Acad. Sci. Paris Sér. A-B**275**(1972), A1057-A1059. MR**46**#9768. MR**0310670 (46:9768)****[6]**W. A. Kirk,*Caristi's fixed point theorem and the theory of normal solvability*, Proc. Seminar on Fixed Point Theory and its Applications, Dalhousie University, 1975 (to appear).**[7]**W. A. Kirk and J. Caristi,*Mapping theorems in metric and Banach spaces*, Bull. Acad. Polon. Sci.**23**(1975). MR**0385654 (52:6514)****[8]**W. A. Kirk,*Caristi's fixed point theorem and metric convexity*(to appear).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1976-0407826-5

Keywords:
Completeness,
lower semicontinuity,
transfinite induction

Article copyright:
© Copyright 1976
American Mathematical Society