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2011-10-04 Nonlinear Seminar

Adam Burchardt
Schauder fixed point, revisited

During the seminar we are going to discuss the following generalization of the classical Schauder fixed point theorem due to R. Cauty:

Let $$ C $$ be a convex subset of a topological vector space $$ E $$. If $$ f \colon C \to C $$ is a continuous function such that $$ f(C) $$ is contained in a compact subset of $$ C $$, then $$ f $$ has a fixed point.

The talk is based on the following paper: R. Cauty, Solution du problème de point fixe de Schauder, Fund. Math. 170 (2001), 231-246.