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An extension of multi-valued contraction mappings and fixed points
Author(s):
Cheng-Kui
Zhong;
Jiang
Zhu;
Pei-Hao
Zhao
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2439-2444.
MSC (2000):
Primary 47H10, 47H04
Posted:
November 24, 1999
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Abstract:
A class of new multi-valued contraction mappings is presented. Under the new contractive conditions, some fixed point theorems for multi-valued self-mappings and nonself-mappings are proved.
References:
- [1]
- J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251. MR 52:15132
- [2]
- S. B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475-487. MR 40:8035
- [3]
- H. W. Yi and Y. C. Zhao, Fixed point theorems for weakly inward multivalued mappings and their randomizations, J. Math. Anal. Appl. 183 (1994), 613-619. MR 95j:47072
- [4]
- V. M. Sehgal and R. E. Smithson, A fixed point theorem for weak directional contraction multifunctions, Math. Japonica, 25 (1980), 345-348. MR 81m:54081
- [5]
- C. K. Zhong, A generalization of Ekeland's variational principle and application to the study of the relation between the weak P. S. condition and coercitvity, Nonlinear Analysis, TMA. 29 (1997), 1421-1431. MR 98j:49036
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Additional Information:
Cheng-Kui
Zhong
Affiliation:
Department of Mathematics, Lanzhou University, Lanzhou 730000, People's Republic of China
Jiang
Zhu
Affiliation:
Department of Mathematics, Lanzhou University, Lanzhou 730000, People's Republic of China
Address at time of publication:
Department of Mathematics, Xuzhou Normal University, Xuzhou 221009, People's Republic of China
Email:
jiangzhu@public.xz.js.cn
Pei-Hao
Zhao
Affiliation:
Department of Mathematics, Lanzhou University, Lanzhou 730000, People's Republic of China
DOI:
10.1090/S0002-9939-99-05318-6
PII:
S 0002-9939(99)05318-6
Received by editor(s):
December 19, 1997
Received by editor(s) in revised form:
September 28, 1998
Posted:
November 24, 1999
Additional Notes:
This research was supprted by the National Science Foundation and Doctoral Foundation of China.
The corresponding author is Jiang Zhu
Communicated by:
David R. Larson
Copyright of article:
Copyright
2000,
American Mathematical Society
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