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

Recommended by Anthony To-Ming Lau

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.