On a conjecture of S. Reich
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- by Peter Z. Daffer, Hideaki Kaneko and Wu Li
- Proc. Amer. Math. Soc. 124 (1996), 3159-3162
- DOI: https://doi.org/10.1090/S0002-9939-96-03659-3
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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
- D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458–464. MR 239559, DOI 10.1090/S0002-9939-1969-0239559-9
- T. H. Chang, Common Fixed Point Theorems for Multi-Valued Mappings, Math. Japonica 41 (1995), 311–320.
- P. Z. Daffer and H. Kaneko, Fixed Points of Generalized Contractive Multi-Valued Mappings, J. Math. Anal. Appl. 192 (1995), 655–666.
- Noriko Mizoguchi and Wataru Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989), no. 1, 177–188. MR 1004592, DOI 10.1016/0022-247X(89)90214-X
- Simeon Reich, Fixed points of contractive functions, Boll. Un. Mat. Ital. (4) 5 (1972), 26–42 (English, with Italian summary). MR 0309095
- Simeon Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 57 (1974), no. 3-4, 194–198 (1975) (English, with Italian summary). MR 397487
- Simeon Reich, Some problems and results in fixed point theory, Topological methods in nonlinear functional analysis (Toronto, Ont., 1982) Contemp. Math., vol. 21, Amer. Math. Soc., Providence, RI, 1983, pp. 179–187. MR 729515, DOI 10.1090/conm/021/729515
- K. P. R. Sastry, S. V. R. Naidu, and J. R. Prasad, Common fixed points for multimaps in a metric space, Nonlinear Anal. 13 (1989), no. 3, 221–229. MR 986445, DOI 10.1016/0362-546X(89)90051-5
Bibliographic 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
- Received by editor(s): April 5, 1995
- Communicated by: Dale Alspach
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3159-3162
- MSC (1991): Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-96-03659-3
- MathSciNet review: 1363454