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Strong Convergence to Solutions for a Class of Variational Inequalities in Banach Spaces by Implicit Iteration Methods

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Abstract

In this paper, in order to solve a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, we introduce two new implicit iteration methods. Their strong convergence is proved, by using new V-mappings instead of W-ones.

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Acknowledgements

The authors are extremely grateful to the referees for their useful comments and suggestions, which helped to improve this paper.

This research is funded by Vietnamese National Foundation of Science and Technology Development.

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Correspondence to Nguyen Buong.

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Communicated by Alejandro Jofré.

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Buong, N., Phuong, N.T.H. Strong Convergence to Solutions for a Class of Variational Inequalities in Banach Spaces by Implicit Iteration Methods. J Optim Theory Appl 159, 399–411 (2013). https://doi.org/10.1007/s10957-013-0350-4

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  • DOI: https://doi.org/10.1007/s10957-013-0350-4

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