Fixed Point Theory and Applications 
Volume 2005 (2005), Issue 2, Pages 169-176
doi:10.1155/FPTA.2005.169

Fixed points of multimaps which are not necessarily nonexpansive

Naseer Shahzad1 and Amjad Lone2

 1Department of Mathematics, Faculty of Sciences, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, College of Sciences, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia
Received 16 October 2004; Revised 3 December 2004

Abstract

Let C be a nonempty closed bounded convex subset of a Banach space X whose characteristic of noncompact convexity is less than 1 and T a continuous 1-χ-contractive SL map (which is not necessarily nonexpansive) from C to KC(X) satisfying an inwardness condition, where KC(X) is the family of all nonempty compact convex subsets of X. It is proved that T has a fixed point. Some fixed points results for noncontinuous maps are also derived as applications. Our result contains, as a special case, a recent result of Benavides and Ramírez (2004).