Strong convergence of a viscosity iterative algorithm in banach spaces with applications

Abstract

© 2016 Suwicha Imnang and Suthep Suantai. We present the strong convergence theorems for the viscosity iterative scheme for finding a common element of the solution set of the system of general variational inequalities for two arbitrary nonlinear mappings and the fixed point set of a nonexpansive mapping in real 2 uniformly smooth and uniformly convex Banach spaces. Furthermore,we apply our main result with the problem of approximating a zero point of accretive operators and a fixed point of strictly pseudocontractive mappings in Banach spaces. The main results presented in this paper improve and extend some results in the literature.