Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-11T12:17:40.657Z Has data issue: false hasContentIssue false
  • English
  • Français

A Uniformly Asymptotically Regular Mapping Without Fixed Points

Published online by Cambridge University Press:  20 November 2018

Pei-kee Lin
Pei-kee Lin*
Affiliation:
Department of Mathematics Memphis State University Memphis, Tennessee 38152
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.

We construct a uniformly asymptotically regular, Lipschitzian mapping acting on a weakly compact convex subset of l2 which has no fixed points.

Keywords

Uniformly asymptotically regularfixed pointLipschitzian47H10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 481 - 483
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Browder, F.E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A., 54 (1965), pp. 1041–1044.Google Scholar
2. Edelstein, M. and Kiang, M.T., On ultimately nonexpansive semigroups, Pacific J. Math. 101 (1982), pp. 93–102.Google Scholar
3. Edelstein, M. and O'Brien, R. C., Nonexpansive mappings, asymptotic regularity and successive approximations, J. London Math. Soc. (2) 17 (1978), pp. 547–554.Google Scholar
4. Goebel, K. and Kirk, W.A., A fixed point theorem for asymptotically nonexpanisve mappings, Proc. Amer. Math Soc. 35 (1972), pp. 171–174.Google Scholar
5. Kiang, M.T. and Tan, K.K., Fixed point theorems for proximately nonexpansive semigroups, Canad. Math. Bull. 29 (2) (1986), pp. 160–166.Google Scholar
6. Kirk, W.A., Fixed point theory for nonexpansive mappings I, II, Lecture Notes in Math . 886, Springer, Berlin, 1981, pp. 484–505 and Contemporary Math #18 AMS Providence, RI 1983, pp. 121–140.Google Scholar
7. Reich, S., The fixed point problem for nonexpansive mappings I, II, Amer. Math. Monthly 83 (1976), pp. 266–268 and 87 (1980), pp. 292-294.Google Scholar
8. Tingley, D., An asymptotically nonexpansive commutative semigroup with no fixed points, Proc. AMS 97 (1986), pp. 107–113.Google Scholar