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

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]**Felix E. Browder,*On a theorem of Caristi and Kirk*, Fixed point theory and its applications (Proc. Sem., Dalhousie Univ., Halifax, N.S., 1975) Academic Press, New York, 1976, pp. 23–27. MR**0461474****[2]**Arne Brøndsted,*On a lemma of Bishop and Phelps*, Pacific J. Math.**55**(1974), 335–341. MR**0380343****[3]**James Caristi,*Fixed point theorems for mappings satisfying inwardness conditions*, Trans. Amer. Math. Soc.**215**(1976), 241–251. MR**0394329**, 10.1090/S0002-9947-1976-0394329-4**[4]**James Caristi and William A. Kirk,*Geometric fixed point theory and inwardness conditions*, The geometry of metric and linear spaces (Proc. Conf., Michigan State Univ., East Lansing, Mich., 1974) Springer, Berlin, 1975, pp. 74–83. Lecture Notes in Math., Vol. 490. MR**0399968****[5]**Ivar Ekeland,*Sur les problèmes variationnels*, C. R. Acad. Sci. Paris Sér. A-B**275**(1972), A1057–A1059 (French). MR**0310670****[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,*Mappings theorems in metric and Banach spaces*, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.**23**(1975), no. 8, 891–894 (English, with Russian summary). MR**0385654****[8]**W. A. Kirk,*Caristi's fixed point theorem and metric convexity*(to appear).

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Additional Information

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

Keywords:
Completeness,
lower semicontinuity,
transfinite induction

Article copyright:
© Copyright 1976
American Mathematical Society