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On a conjecture of S. Reich
Author(s):
Peter
Z.
Daffer;
Hideaki
Kaneko;
Wu
Li
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3159-3162.
MSC (1991):
Primary 47H10
MathSciNet review:
1363454
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Abstract:
Simeon Reich (1974) proved that the fixed point theorem for single-valued mappings proved by Boyd and Wong can be generalized to multivalued mappings which map points into compact sets. He then asked (1983) whether his theorem can be extended to multivalued mappings whose range consists of bounded closed sets. In this note, we provide an affirmative answer for a certain subclass of Boyd-Wong contractive mappings.
References:
- 1.
- D. W. Boyd and J. S. W. Wong, On Nonlinear Contractions, Proc. A.M.S. 89(1968), 458-464. MR 39:916
- 2.
- T. H. Chang, Common Fixed Point Theorems for Multi-Valued Mappings,Math. Japonica 41 (1995), 311--320. CMP 1995:11
- 3.
- P. Z. Daffer and H. Kaneko, Fixed Points of Generalized Contractive Multi-Valued Mappings,J. Math. Anal. Appl. 192 (1995), 655--666. CMP 1995:12
- 4.
- N. Mizoguchi and W. Takahashi, Fixed Points Theorems for Multi-Valued Mappings on Complete Metric Spaces,J. Math. Anal. Appl. 141(1989) 177-188. MR 90f:47086
- 5.
- S. Reich, Fixed Points of Contractive Functions, Boll. Un. Mat. Ital., (4) 5 (1972), 26-42. MR 46:8206
- 6.
- S. Reich, Some Fixed Point Problems,Atti. Accad. Naz. Lincei, 57(1974), 194-198. MR 53:1346
- 7.
- S. Reich, Some Problems and Results in Fixed Point Theory,Contemporary Math. A.M.S. 21(1983), 179--187. MR 85e:47082
- 8.
- K. Sastry, S. Naidu and J. Prasad, Common Fixed Points for Mutimaps in a Metric Space,Nonlinear Anal. 13(3) (1989) 221-229. MR 90b:54034
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Additional Information:
Peter
Z.
Daffer
Affiliation:
Department of Mathematics, Macon College, Macon, Georgia 31297
Email:
pdaffer@cennet.mc.peachnet.edu
Hideaki
Kaneko
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23529-0077
Email:
kaneko@math.odu.edu
Wu
Li
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23529-0077
Email:
wuli@math.odu.edu
DOI:
10.1090/S0002-9939-96-03659-3
PII:
S 0002-9939(96)03659-3
Received by editor(s):
April 5, 1995
Communicated by:
Dale Alspach
Copyright of article:
Copyright
1996,
American Mathematical Society
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