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The aim of this paper is to introduce the generalized viscosity implicit rules of one nonexpansive mapping in uniformly smooth Banach spaces. Strong convergence theorems of the rules are proved under certain assumptions imposed on the parameters. As applications, we use our main results to solve fixed point problems of strict pseudocontractions in Hilbert spaces and variational inequality problems in Hilbert spaces. Finally, we also give one numerical example to support our main results. c ©2016 All rights reserved.

Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces