Open Access

Fixed points of multimaps which are not necessarily nonexpansive

Fixed Point Theory and Applications20052005:286519

https://doi.org/10.1155/FPTA.2005.169

Received: 16 October 2004

Published: 30 June 2005

Abstract

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

(1)
Department of Mathematics, Faculty of Sciences, King Abdul Aziz University
(2)
Department of Mathematics, College of Sciences, King Khalid University

Copyright

© Shahzad and Lone 2005