Strong Convergence to a Solution of a Variational Inequality Problem in Banach SpacesReport as inadecuate




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Journal of Applied MathematicsVolume 2014 2014, Article ID 346517, 10 pages

Research Article

Department of Information Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan

Sundai Preparatory School, Surugadai, Kanda, Chiyoda-ku, Tokyo 101-8313, Japan

Received 22 January 2014; Accepted 14 May 2014; Published 9 June 2014

Academic Editor: Luigi Muglia

Copyright © 2014 Yasunori Kimura and Kazuhide Nakajo. 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.

Abstract

We consider the variational inequality problem for afamily of operators of a nonempty closed convex subset of a 2-uniformly convex Banach space with a uniformly Gâteaux differentiable norm, into its dual space. We assume some properties for the operators and get strong convergence to a common solution to the variational inequality problem by the hybridmethod proposed by Haugazeau. Using these results, we obtain several resultsfor the variational inequality problem and the proximal point algorithm.





Author: Yasunori Kimura and Kazuhide Nakajo

Source: https://www.hindawi.com/



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