Approximating solutions of the sum of a finite family of maximally monotone mappings in Hilbert spaces

The purpose of this paper is to study the method of approximation for a zero of the sum of a finite family of maximally monotone mappings using viscosity type Douglas–Rachford splitting algorithm and prove some strong convergence theorems of the proposed algorithm under suitable conditions. In addition, we give some applications to the minimization problems. Finally, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.