The fixed point property and unbounded sets in Hilbert space-Reference-Cited by-同舟云学术

The fixed point property and unbounded sets in Hilbert space

Published:1980 Issue:2 Volume:258 Page:531-537
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Ray William O.

Abstract

It is shown that a closed convex subset K of a real Hilbert space H has the fixed point property for nonexpansive mappings if and only if K is bounded.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1980-258-02/S0002-9947-1980-0558189-1/S0002-9947-1980-0558189-1.pdf

Reference5 articles.

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

2. A contribution to the theory of nonexpansive mappings;Goebel, K.;Bull. Calcutta Math. Soc.,1978

3. Zum Prinzip der kontraktiven Abbildung;Göhde, Dietrich;Math. Nachr.,1965

4. A fixed point theorem for mappings which do not increase distances;Kirk, W. A.;Amer. Math. Monthly,1965

5. Nonexpansive mappings on unbounded convex domains;Ray, William O.;Bull. Acad. Polon. Sci. S\'{e}r. Sci. Math. Astronom. Phys.,1978

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