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Fixed point theorems in locally convex spaces—the Schauder mapping method

By S. Cobza&#351

Abstract

In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962) a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory

Topics: Mathematics, QA1-939, Science, Q, DOAJ:Mathematics, DOAJ:Mathematics and Statistics, Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433
Publisher: Springer
Year: 2006
DOI identifier: 10.1155/FPTA
OAI identifier: oai:doaj.org/article:0ab4f549aea342d89e709295cd997834
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