Open Access

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

Fixed Point Theory and Applications20062006:57950

DOI: 10.1155/FPTA/2006/57950

Received: 22 March 2005

Accepted: 6 September 2005

Published: 12 March 2006

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.

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Authors’ Affiliations

(1)
Faculty of Mathematics and Computer Science, Babeş-Bolyai University

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Copyright

© S. Cobzaş. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.