Viscosity approximation methods based on generalized contraction mappings for a countable family of strict pseudo-contractions, a general system of variational inequalities and a generalized mixed equilibrium problem in Banach spaces

In this paper, we introduce viscosity approximation methods based on generalized contractionmappings for finding a set of common fixed points of a countable family of strict pseudo-contractionmappings, the commonelement of the set solutions of a general system of variational inequalities with Lipschitzian and relaxed cocoercive mappings and the set of solutions of a generalizedmixed equilibrium problem. Furthermore, strong convergence theorems of the purposed iterative process are established in the framework of Banach spaces. The results presented in this paper improve and extend many recent important results. © 2013 Elsevier Ltd. All rights reserved.