Strong convergence theorems for variational inequality problems and fixed point problems in uniformly smooth and uniformly convex Banach spaces

Gang Cai () and Shangquan Bu ()

Journal of Global Optimization, 2013, vol. 56, issue 4, 1529-1542

Abstract: In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a general variational inequality problem for finite inverse-strongly accretive mappings and the set of common fixed points for a nonexpansive mapping in a uniformly smooth and uniformly convex Banach space. We obtain a strong convergence theorem under some suitable conditions. Our results improve and extend the recent ones announced by many others in the literature. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Strong convergence; Variational inequality; Fixed point; Nonexpansive mapping; Banach space; 47H09; 47H10 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9923-2

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