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A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings

Published online by Cambridge University Press:  20 November 2018

Hong-Kun Xu
Hong-Kun Xu*
Affiliation:
Department of Mathematics, East China Institute of Chemical Technology, Shanghai 200237, People's Republic of China
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Abstract

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As a generalization of Kiang and Tan's proximately nonexpansive semigroups, the notion of a proximately uniformly Lipschitzian semigroup is introduced and an existence theorem of common fixed points for such a semigroup is proved in a Banach space whose characteristic of convexity is less than one.

Keywords

47H10Common fixed pointproximately uniformly Lipschitzian semigroup
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 559 - 562
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Downing, D. and Turett, B., Some properties of the characteristic of convexity relating to fixed point theory, Pacific J. Math. 104 (1984), 343–350.Google Scholar
2. Edelstein, M. andM. Kiang, T., On ultimately nonexpansive semigroup, Pacific J. Math. 101 (1982), 93–102.Google Scholar
3. Edelstein, M. andM. Kiang, T., A common fixed point theorem in reflexive locally uniformly convex Banach spaces, Proc. Amer. Math. Soc. 94 (1985), 411–415.Google Scholar
4. Goebel, K. and Reich, S., Uniform convexity, hyperbolic geometry and nonexpansive mappings. Marcel Dekker, New York-Basel, 1984.Google Scholar
5. Kiang, M. T., A fixed point theorem for eventually nonexpansive semigroups of mappings, J. Math. Anal. Appl. 56 (1976), 567–569.Google Scholar
6. Kiang, M. T. and Tan, K. K., Fixed point theorems for proximately nonexpansive semigroups, Canad. Math. Bull. 29 (1986), 160–166.Google Scholar
7. Lifschitz, E. A., Fixed point theorems for operators in strongly convex spaces, Vornez Gos. Univ. Trudy, Mat. Fak. 10 (1975), 23–28 (in Russian).Google Scholar
8. Turett, B., A dual view of a theorem of Bâillon, in Nonlinear Analysis and Applications, (S. P. Singh and Burry, L. H., eds.), Marcel Dekker, New York-Basel, 1982, 279–286.Google Scholar