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An Iteration Method for Nonexpansive Mappings in Hilbert Spaces

Fixed Point Theory and Applications volume 2007, Article number: 028619 (2006) Cite this article

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

    Lin Wang

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  1. Lin Wang
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Correspondence to Lin Wang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wang, L. An Iteration Method for Nonexpansive Mappings in Hilbert Spaces. Fixed Point Theory Appl 2007, 028619 (2006). https://doi.org/10.1155/2007/28619

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