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Remarks on some fixed point theorems
Author:
Teck Cheong Lim
Journal:
Proc. Amer. Math. Soc. 60 (1976), 179-182
MSC:
Primary 47H10; Secondary 54H25
MathSciNet review:
0423139
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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]
James
Caristi, Fixed point theorems for mappings
satisfying inwardness conditions, Trans. Amer.
Math. Soc. 215
(1976), 241–251. MR 0394329
(52 #15132), http://dx.doi.org/10.1090/S0002-9947-1976-0394329-4
- [2]
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
(53 #3806)
- [3]
Michael
Edelstein, Fixed point theorems in uniformly
convex Banach spaces, Proc. Amer. Math.
Soc. 44 (1974),
369–374. MR 0358451
(50 #10917), http://dx.doi.org/10.1090/S0002-9939-1974-0358451-4
- [4]
John
L. Kelley, General topology, D. Van Nostrand Company, Inc.,
Toronto-New York-London, 1955. MR 0070144
(16,1136c)
- [5]
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
(52 #6514)
- [6]
Teck
Cheong Lim, Characterizations of normal
structure, Proc. Amer. Math. Soc. 43 (1974), 313–319. MR 0361728
(50 #14173), http://dx.doi.org/10.1090/S0002-9939-1974-0361728-X
- [7]
Teck
Cheong Lim, 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), http://dx.doi.org/10.1090/S0002-9904-1974-13640-2
- [8]
Chi
Song Wong, On a fixed point theorem of
contractive type, Proc. Amer. Math. Soc.
57 (1976), no. 2,
283–284. MR 0407826
(53 #11596), http://dx.doi.org/10.1090/S0002-9939-1976-0407826-5
- [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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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1976-0423139-X
PII:
S 0002-9939(1976)0423139-X
Article copyright:
© Copyright 1976 American Mathematical Society
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