Strong convergence of a splitting proximal projection method for the sum of two maximal monotone operators

In this paper, combining the new splitting method proposed by Eckstein and Svaiter and the forcing strong convergence method of Solodov and Svaiter, we propose a splitting proximal projection method for the sum of two maximal monotone operators. We prove that the proposed method is well-defined whether the solution set of the problem is nonempty or not and the sequence generated by the method converges strongly to an extended solution of the problem.