Open Access

An Iteration Method for Nonexpansive Mappings in Hilbert Spaces

Fixed Point Theory and Applications20062007:028619

DOI: 10.1155/2007/28619

Received: 22 August 2006

Accepted: 2 November 2006

Published: 26 December 2006

Abstract

In real Hilbert space , from an arbitrary initial point , an explicit iteration scheme is defined as follows: , where , is a nonexpansive mapping such that is nonempty, is a -strongly monotone and -Lipschitzian mapping, , and . Under some suitable conditions, the sequence is shown to converge strongly to a fixed point of and the necessary and sufficient conditions that converges strongly to a fixed point of are obtained.

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Authors’ Affiliations

(1)
Department of Mathematics, Kunming Teachers College

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Copyright

© Lin Wang. 2007

This article is published under license to BioMed Central Ltd. 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.