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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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  • Nguyen Buong

    (VAST)

  • Nguyen Thi Hong Phuong

    (VAST)

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.

Suggested Citation

  • Nguyen Buong & Nguyen Thi Hong Phuong, 2013. "Strong Convergence to Solutions for a Class of Variational Inequalities in Banach Spaces by Implicit Iteration Methods," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 399-411, November.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:2:d:10.1007_s10957-013-0350-4
    DOI: 10.1007/s10957-013-0350-4
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    References listed on IDEAS

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    1. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    2. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
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