Fixed-point theorems in infinite-dimensional spaces: Difference between revisions

Revision as of 08:37, 6 May 2004

Revision as of 08:37, 6 May 2004

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The '''Schauder fixed point theorem''' states, in one version, that if ''C'' is a [[nonempty]] [[closed set|closed]] [[convex]] subset of a [[Banach space]] ''V'' and ''f'' is a continuous map from ''C'' to ''C'' whose image is [[compact|countably compact]], then ''f'' has a fixed point.

The '''Tikhonov (Tychohoff) fixed point theorem''' is now applied to any [[locally convex topological vector space]] ''V''. For any non-empty [[compact]] convex set ''X'' in ''V'', and [[continuous function]]