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

Revision as of 16:57, 16 September 2006

Revision as of 11:19, 25 September 2006

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

:''f'':''X'' →→ ''X'',

there is a fixed point for ''f''.

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* Vasile I. Istratescu, ''Fixed Point Theory, An Introduction'', D.Reidel, Holland (1981). ISBN 90-277-1224-7.

* Andrzej Granas and James Dugundji, ''Fixed Point Theory'' (2003) Springer-Verlag, New York, ISBN 0-387-00173-5.

* William A. Kirk and Brailey Sims, ''Handbook of Metric Fixed Point Theory'' (2001), Kluwer Academic, London ISBN 0-7923-7073-2.

[[Category:Fixed points]]

[[Category:Functional analysis]]

[[Category:Mathematical theorems]]

[[fr:Théorème du point fixe de Schauder]]

[[pl:Twierdzenie Schaudera o punkcie stałym]]