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

Revision as of 13:33, 5 June 2005

Revision as of 13:42, 5 June 2005

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Kakutani's fixed point theorem states that :

''Every upper semi-continuous correspondence that maps a compact convex subset of a locally convex space into itself with a closed graph and convex nonempty images has a fixed point.''

It can be seen as an application of Brouwer's fixed point theorem.