Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 16028, 5 pages
doi:10.1155/2007/16028
Research Article

Remarks on Extensions of the Himmelberg Fixed Point Theorem

Hidetoshi Komiya1 and Sehie Park2,3

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

Received 30 August 2007; Accepted 16 November 2007

Academic Editor: Anthony To-Ming Lau

Copyright © 2007 Hidetoshi Komiya and Sehie Park. 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.

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 𝔅 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.