A fixed point free nonexpansive map-Reference-Cited by-同舟云学术

A fixed point free nonexpansive map

Published:1981 Issue:3 Volume:82 Page:423-424
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Alspach Dale E.

Abstract

In this note we give an example of a weakly compact convex subset of L 1 [ 0 , 1 ] {L_1}[0,1] that fails to have the fixed point property for nonexpansive maps. This answers a long-standing question which was recently raised again by S. Reich [7].

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1981-082-03/S0002-9939-1981-0612733-0/S0002-9939-1981-0612733-0.pdf

Reference7 articles.

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2. Nonexpansive nonlinear operators in a Banach space;Browder, Felix E.;Proc. Nat. Acad. Sci. U.S.A.,1965

3. N. Dunford and J. T. Schwartz, Linear operators: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958.

4. E. Hopf, Ergodentheorie, Ergebnisse der Math., Vol. 5, Springer-Verlag, Berlin, 1937.

5. On nonexpansive mappings;Karlovitz, L. A.;Proc. Amer. Math. Soc.,1976

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