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Open Access

A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings

Journal of Inequalities and Applications20092009:520301

Received: 3 June 2009

Accepted: 1 November 2009

Published: 4 November 2009


A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.


Hilbert SpaceApproximation MethodVariational InequalityConvergence TheoremMonotone Mapping

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Authors’ Affiliations

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand


© C. Klin-eam and S. Suantai 2009

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.