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

Revision as of 09:00, 1 June 2004

Revision as of 14:08, 26 December 2004

Line 6:

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 (TychohoffTychonoff) 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]]

:''f'':''X'' → ''X'',