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  • Research Article
  • Open Access

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

Fixed Point Theory and Applications20062006:57950

https://doi.org/10.1155/FPTA/2006/57950

  • Received: 22 March 2005
  • Accepted: 6 September 2005
  • Published:

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.

Keywords

  • Functional Analysis
  • Game Theory
  • Point Theorem
  • Mapping Method
  • Differential Geometry

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Authors’ Affiliations

(1)
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania

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