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

Gang Cai () and Shangquan Bu ()

Journal of Global Optimization, 2013, vol. 55, issue 2, 437-457

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

Keywords: Strong convergence; Fixed point; Nonexpansive mapping; Variational inequality; Banach space; 47H09; 47H10 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9883-6

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