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  • Research Article
  • Open Access

General Iterative Algorithm for Nonexpansive Semigroups and Variational Inequalities in Hilbert Spaces

Journal of Inequalities and Applications20102010:264052

https://doi.org/10.1155/2010/264052

  • Received: 24 October 2009
  • Accepted: 12 February 2010
  • Published:

Abstract

We introduce a general iterative method for finding the solution of the variational inequality problem over the fixed point set of a nonexpansive semigroup in a Hilbert space. We prove that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions. Our results improve and generalize many known corresponding results.

Keywords

  • Hilbert Space
  • Variational Inequality
  • Iterative Method
  • Iterative Algorithm
  • Common Element

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Authors’ Affiliations

(1)
Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, China
(2)
Department of Foundation, Xian Communication Institute, Xian, 710106, China

Copyright

© Jinlong Kang et al. 2010

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.

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