Une généralisation de la conjecture de point fixe de Schauder release_5jjpumvq4jbb7m2bc34ohl4b5q

Abstract

We prove the following generalisation of Schauder's fixed point conjecture: Let C_1,...,C_n be convex subsets of a Hausdorff topological vector space. Suppose that the C_i are closed in C=C_1∪...∪ C_n. If f:C→ C is a continuous function whose image is contained in a compact subset of C, then its Lefschetz number Λ(f) is defined. If Λ(f)0, then f has a fixed point.
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