Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 28619, 8 pages
Research Article

An Iteration Method for Nonexpansive Mappings in Hilbert Spaces

Lin Wang

Department of Mathematics, Kunming Teachers College, Kunming, Yunnan 650031, China

Received 22 August 2006; Revised 2 November 2006; Accepted 2 November 2006

Academic Editor: Nan-Jing Huang

Copyright © 2007 Lin Wang. 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.


In real Hilbert space H, from an arbitrary initial point x0H, an explicit iteration scheme is defined as follows: xn+1=αnxn+(1αn)Tλn+1xn,n0, where Tλn+1xn=Txnλn+1μF(Txn), T:HH is a nonexpansive mapping such that F(T)={xK:Tx=x} is nonempty, F:HH is a η-strongly monotone and k-Lipschitzian mapping, {αn}(0,1), and {λn}[0,1). Under some suitable conditions, the sequence {xn} is shown to converge strongly to a fixed point of T and the necessary and sufficient conditions that {xn} converges strongly to a fixed point of T are obtained.