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

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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Article ID: iaor20131210
Volume: 55
Issue: 2
Start Page Number: 437
End Page Number: 457
Publication Date: Feb 2013
Journal: Journal of Global Optimization
Authors: ,
Keywords: vector optimization, Banach space, mapping
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.

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