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  • Research Article
  • Open Access

Remarks on Extensions of the Himmelberg Fixed Point Theorem

Fixed Point Theory and Applications20072007:016028

https://doi.org/10.1155/2007/16028

  • Received: 30 August 2007
  • Accepted: 16 November 2007
  • Published:

Abstract

Recently, Jafari and Sehgal obtained an extension of the Himmelberg fixed point theorem based on the Kakutani fixed-point theorem. We give generalizations of the extension to almost convex sets instead of convex sets. We also give generalizations for a large class of better admissible multimaps instead of the Kakutani maps. Our arguments are based on the KKM principle and some of previous results due to the second author.

Keywords

  • Point Theorem
  • Differential Geometry
  • Computational Biology

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Authors’ Affiliations

(1)
Faculty of Business and Commerce, Keio University, Hiyoshi, Yokohama 223-8521, Japan
(2)
The National Academy of Sciences, Seocho-gu, Seoul, 137-044, Korea
(3)
Department of Mathematical Sciences, College of Natural Science, Seoul National University, Seoul, 151-747, Korea

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