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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This work was supported by the NSF of China (No.11171172).
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Cai, G., Bu, S. Modified extragradient methods for variational inequality problems and fixed point problems for an infinite family of nonexpansive mappings in Banach spaces. J Glob Optim 55, 437–457 (2013). https://doi.org/10.1007/s10898-012-9883-6
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DOI: https://doi.org/10.1007/s10898-012-9883-6