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Extragradient Method for Solutions of Variational Inequality Problems in Banach Spaces

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  • H. Zegeye
  • N. Shahzad

Abstract

We introduce an iterative process which converges strongly to solutions of a certain variational inequity problem for η‐inverse strongly accretive mappings in the set of common fixed points of finite family of strictly pseudocontractive mappings in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

Suggested Citation

  • H. Zegeye & N. Shahzad, 2013. "Extragradient Method for Solutions of Variational Inequality Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:832548
    DOI: 10.1155/2013/832548
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    References listed on IDEAS

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    1. Yonghong Yao & Yeong-Cheng Liou & Cun-Lin Li & Hui-To Lin, 2012. "Extended Extragradient Methods for Generalized Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Yonghong Yao & Yeong-Cheng Liou & Cun-Lin Li & Hui-To Lin, 2012. "Extended Extragradient Methods for Generalized Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, November.
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    Cited by:

    1. Phayap Katchang & Somyot Plubtieng, 2014. "The Hybrid Projection Methods for Pseudocontractive, Nonexpansive Semigroup, and Monotone Mapping," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Mohammed Ali Alghamdi & Naseer Shahzad & Habtu Zegeye, 2014. "On Solutions of Variational Inequality Problems via Iterative Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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