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

Abdul Rahim Khan

 Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Received 15 September 2004; Revised 21 November 2004

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.