Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 16028, 5 pages
doi:10.1155/2007/16028
Remarks on extensions of the Himmelberg fixed point theorem
Hidetoshi Komiya1
and Sehie Park2
1Faculty of Business and Commerce, Keio University, Hiyoshi, Yokohama, 223-8521, Japan
2The National Academy of Sciences, Seocho-gu, Seoul 137-044, Korea
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.