On nonexpansive mappings

Karlovitz, L A.

doi:10.1090/S0002-9939-1976-0405182-X

On nonexpansive mappings
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Proc. Amer. Math. Soc. 55 (1976), 321-325 Request permission

Abstract:

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

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Examples of spaces which do not contain

and whose duals are not separable

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