Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-10T11:14:59.796Z Has data issue: false hasContentIssue false
  • English
  • Français

Fixed Point Theorems for Lipspchitzian Semigroups

Published online by Cambridge University Press:  20 November 2018

Hajime ishihara
Hajime ishihara*
Affiliation:
Department of Information Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let U be a nonempty subset of a Banach space, S a left reversible semitopological semigroup, a continuous representation of S as lipschitzian mappings on U into itself, that is for each s ∊ S, there exists ks > 0 such that for x, y ∊ U. We first show that if there exists a closed subset C of U such that then S with lim sups has a common fixed point in a Hilbert space. Next, we prove that the theorem is valid in a Banach space E if lim sups

Keywords

47H1054H25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 90 - 97
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Bae, J. S., Reflexivity of a Banach space with a uniformly normal structure, Proc. Amer. Math. Soc. 90 (1984), 269–270. Google Scholar
2. Bynum, W. L., Normal structure coefficients for Banach spaces, Pacific J. Math. 86 (1980), 427^36.Google Scholar
3. Casini, E. and Maluta, E., Fixed points of uniformly lipschitzian mappings in spaces with uniformly normal structure, Nonlinear Analysis 9 (1985), 103–108. Google Scholar
4. Downing, D. J. and Ray, W. O., Uniformly lipschitzian semigroup in Hilbert space, Canad. Math. Bull. 25 (1982), 210–214. Google Scholar
5. Goebel, K. and W. Kirk, A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174. Google Scholar
6. Goebel, K. and W. Kirk, A., A fixed point theorem for transformations whose iterates have uniform Lipschitz constant, Studia Math. 47 (1973), 135–140. Google Scholar
7. Goebel, K., Kirk, W. A. and Thele, R. L., Uniformly lipschitzian families of transformations in Banach spaces, Can. J. Math. 26 (1974), 1245–1256. Google Scholar
8. Ishihara, H. and W., Takahashi, Fixed point theorems for uniformly lipschitzian semigroups in Hilbert spaces, J. Math. Anal. Appl. 127 (1987), 206–210.Google Scholar
9. Ishihara, H. and W., Takahashi, Modulus of convexity, characteristic of convexity and fixed point theorems, Kodai Math J. 10 (1987), 197–208. Google Scholar
10. Lifschitz, E. A., Fixed point theorems for operators in strongly convex spaces, Voronez Gos. Univ. Trudy Math. Fak. 16 (1975), 23–28. Google Scholar
11. Lim, T. C, On asymptotic centers and fixed points of nonexpansive mappings, Can. J. Math. 32 (1980), 421–430. Google Scholar
12. Maluta, E., Uniformly normal structure and related coefficients, Pacific J. Math. IIII (1984), 357– 369.Google Scholar