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By use of a new viscosity approximation method, we construct an explicit iterative algorithm for finding common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in the framework of Banach spaces. A strong convergence theorem is obtained for solving a kind of variational inequality problems. Our results improve and extend the corresponding ones of other authors with related interest. c ©2016 All rights reserved.

A new viscosity approximation method for common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in Banach spaces