Open Access

Convergence theorems for fixed points of demicontinuous pseudocontractive mappings

Fixed Point Theory and Applications20052005:475373

https://doi.org/10.1155/FPTA.2005.67

Received: 26 August 2004

Published: 28 April 2005

Abstract

Let be an open subset of a real uniformly smooth Banach space . Suppose is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where denotes the closure of . Then, it is proved that (i) for every ; (ii) for a given , there exists a unique path , , satisfying . Moreover, if or there exists such that the set is bounded, then it is proved that, as , the path converges strongly to a fixed point of . Furthermore, explicit iteration procedures with bounded error terms are proved to converge strongly to a fixed point of .

Authors’ Affiliations

(1)
The Abdus Salam International Centre for Theoretical Physics

Copyright

© Chidume and Zegeye 2005