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


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.


Authors’ Affiliations

Department of Mathematics, Kunming Teachers College


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© Lin Wang. 2007

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