The Fixed Point Theorems of Brouwer and Schauder

We are going to dedicate the first chapter to the study of the fixed point theorem of Schauder [S, 1930]. We have divided the chapter into two parts: In the first part we give the finite dimensional version of Schauder’s fixed point theorem (usually known as Brouwer’s theorem [Br, 1912], though an equivalent form had been proved by Poincaré [Po, 1886]). These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.