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Strong Convergence to a Solution of a Variational Inequality Problem in Banach Spaces

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  • Yasunori Kimura
  • Kazuhide Nakajo

Abstract

We consider the variational inequality problem for a family 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 hybrid method proposed by Haugazeau. Using these results, we obtain several results for the variational inequality problem and the proximal point algorithm.

Suggested Citation

  • Yasunori Kimura & Kazuhide Nakajo, 2014. "Strong Convergence to a Solution of a Variational Inequality Problem in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:346517
    DOI: 10.1155/2014/346517
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    References listed on IDEAS

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    1. Heinz H. Bauschke & Patrick L. Combettes, 2001. "A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 248-264, May.
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