Remarks on some fixed point theorems

Author:
Teck Cheong Lim

Journal:
Proc. Amer. Math. Soc. **60** (1976), 179-182

MSC:
Primary 47H10; Secondary 54H25

DOI:
https://doi.org/10.1090/S0002-9939-1976-0423139-X

MathSciNet review:
0423139

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Abstract | References | Similar Articles | Additional Information

Abstract: A compact Hausdorff pseudo-topology is introduced on every closed convex bounded subset of a uniformly convex Banach space and is used to prove a previous theorem of the author.

**[1]**J. Caristi,*Fixed point theorems for mappings satisfying inwardness conditions*(to appear). MR**0394329 (52:15132)****[2]**J. Caristi and W. A. Kirk,*Geometric fixed point theory and inwardness conditions*(to appear). MR**0399968 (53:3806)****[3]**M. Edelstein,*Fixed point theorems in uniformly convex Banach spaces*, Proc. Amer. Math. Soc.**44**(1974), 369-374. MR**50**# 10917. MR**0358451 (50:10917)****[4]**J. L. Kelley,*General topology*, Van Nostrand, Princeton, N. J., 1955. MR**16**, 1136. MR**0070144 (16:1136c)****[5]**W. A. Kirk and J. Caristi,*Mapping theorems in metric and Banach spaces*(to appear). MR**0385654 (52:6514)****[6]**T. C. Lim,*Characterizations of normal structure*, Proc. Amer. Math. Soc.**43**(1974), 313-319. MR**50**#14173. MR**0361728 (50:14173)****[7]**-,*A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space*, Bull. Amer. Math. Soc.**80**(1974), 1123-1126. MR**0394333 (52:15136)****[8]**Chi Song 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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DOI:
https://doi.org/10.1090/S0002-9939-1976-0423139-X

Article copyright:
© Copyright 1976
American Mathematical Society