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  • Research Article
  • Open Access

Fixed points of multimaps which are not necessarily nonexpansive

Fixed Point Theory and Applications20052005:286519

  • Received: 16 October 2004
  • Published:


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, P.O. Box 80203 Jeddah, 21589, Saudi Arabia
Department of Mathematics, College of Sciences, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia


© Shahzad and Lone 2005