On nonexpansive mappings

Author:

Karlovitz L A.

Abstract

A generalized Hilbert space property is used to analyze nonexpansive mappings in certain settings. In particular it is shown that in l 1 {l_1} and in the important, recently defined, space J 0 {J_0} , a nonexpansive self-mapping of a bounded weak ^{\ast } closed convex subset has a fixed point.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference10 articles.

1. Orthogonality in linear metric spaces;Birkhoff, Garrett;Duke Math. J.,1935

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

3. The solution by iteration of linear functional equations in Banach spaces;Browder, F. E.;Bull. Amer. Math. Soc.,1966

4. Über Fixpunkte bei stetigen Selbstabbildungen mit kompakten Iterierten;Göhde, Dietrich;Math. Nachr.,1964

5. Orthogonality and linear functionals in normed linear spaces;James, Robert C.;Trans. Amer. Math. Soc.,1947

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