General iteration scheme for finding the common fixed points of an infinite family of nonexpansive mappings

The purpose of this paper is to suggest and analyze the general viscosity iteration scheme for an infinite family of nonexpansive mappings \(\{T_i\}^\infty_{i=1}\). Additionally, it proves that this iterative scheme converges strongly to a common fixed point of \(\{T_i\}^\infty_{i=1}\) in the framework of reflexive and smooth convex Banach space,which solves some variational inequality. Results proved in this paper improve and generalize recent known results in the literature.