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Remarks on Extensions of the Himmelberg Fixed Point Theorem

Fixed Point Theory and Applications volume 2007, Article number: 016028 (2007) Cite this article

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.

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Authors and Affiliations

  1. Faculty of Business and Commerce, Keio University, Hiyoshi, Yokohama, 223-8521, Japan

    Hidetoshi Komiya

  2. The National Academy of Sciences, Seocho-gu, Seoul, 137-044, Korea

    Sehie Park

  3. Department of Mathematical Sciences, College of Natural Science, Seoul National University, Seoul, 151-747, Korea

    Sehie Park

Authors
  1. Hidetoshi Komiya
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  2. Sehie Park
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Correspondence to Hidetoshi Komiya.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Komiya, H., Park, S. Remarks on Extensions of the Himmelberg Fixed Point Theorem. Fixed Point Theory Appl 2007, 016028 (2007). https://doi.org/10.1155/2007/16028

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

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