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Modified extragradient methods for variational inequality problems and fixed point problems for an infinite family of nonexpansive mappings in Banach spaces

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  • Gang Cai
  • Shangquan Bu

Abstract

In this paper, we introduce a new general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of a general variational inequality for two inverse-strongly accretive mappings in Banach space. We obtain some strong convergence theorems by a modified extragradient method under suitable conditions. Our results extend the recent results announced by many others. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Gang Cai & Shangquan Bu, 2013. "Modified extragradient methods for variational inequality problems and fixed point problems for an infinite family of nonexpansive mappings in Banach spaces," Journal of Global Optimization, Springer, vol. 55(2), pages 437-457, February.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:2:p:437-457
    DOI: 10.1007/s10898-012-9883-6
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    References listed on IDEAS

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    1. Lu-Chuan Ceng & Chang-yu Wang & Jen-Chih Yao, 2008. "Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 375-390, June.
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