Open Access

Remarks on Extensions of the Himmelberg Fixed Point Theorem

Fixed Point Theory and Applications20072007:016028

DOI: 10.1155/2007/16028

Received: 30 August 2007

Accepted: 16 November 2007

Published: 13 December 2007


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.


Authors’ Affiliations

Faculty of Business and Commerce, Keio University, Hiyoshi
The National Academy of Sciences, Seocho-gu
Department of Mathematical Sciences, College of Natural Science, Seoul National University


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© H. Komiya and S. Park. 2007

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.