Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 3, Pages 323-331
doi:10.1155/JAMSA.2005.323
Properties of fixed point set of a multivalued map
Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Received 15 September 2004; Revised 21 November 2004
Copyright © 2005 Abdul Rahim Khan. 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
Properties of the set of fixed points of some discontinuous multivalued maps in a strictly convex Banach space are studied; in particular, affirmative answers are provided to the questions related to set of fixed points and posed by Ko in 1972 and Xu and Beg in 1998. A result regarding the existence of best approximation is derived.