An iterative algorithm with applications for solving variational inclusion problems and nonexpansive mappings

In this paper, a viscosity splitting iterative algorithm with perturbation is introduced for solving an inclusion problem with two accretive operators and a fixed point problem of an infinite family of nonexpansive mappings. Strong convergence of the iterative algorithm is obtained in a Banach space. A convex minimization problem is also considered in Hilbert spaces as an applications.