Fixed Point Theory and Applications
Volume 2005 (2005), Issue 1, Pages 67-77

Convergence theorems for fixed points of demicontinuous pseudocontractive mappings

C. E. Chidume and H. Zegeye

The Abdus Salam International Centre for Theoretical Physics, Trieste 34014, Italy

Received 26 August 2004

Copyright © 2005 C. E. Chidume and H. Zegeye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let D be an open subset of a real uniformly smooth Banach space E. Suppose T:D¯E is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where D¯ denotes the closure of D. Then, it is proved that (i) D¯(I+r(IT)) for every r>0; (ii) for a given y0D, there exists a unique path tytD¯, t[0,1], satisfying yt:=tTyt+(1t)y0. Moreover, if F(T) or there exists y0D such that the set K:={yD:Ty=λy+(1λ)y0 for λ>1} is bounded, then it is proved that, as t1, the path {yt} converges strongly to a fixed point of T. Furthermore, explicit iteration procedures with bounded error terms are proved to converge strongly to a fixed point of T.