Zakład Optymalizacji i Sterowania: 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.