Open Access

Fixed points of multimaps which are not necessarily nonexpansive

Fixed Point Theory and Applications20052005:286519

Received: 16 October 2004

Published: 30 June 2005


Let be a nonempty closed bounded convex subset of a Banach space whose characteristic of noncompact convexity is less than and a continuous - -contractive map (which is not necessarily nonexpansive) from to satisfying an inwardness condition, where is the family of all nonempty compact convex subsets of . It is proved that 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).

Authors’ Affiliations

Department of Mathematics, Faculty of Sciences, King Abdul Aziz University
Department of Mathematics, College of Sciences, King Khalid University


© Shahzad and Lone 2005