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

Abstract

In this paper, a projective-splitting method is proposed for finding a zero of the sum of \(n\) maximal monotone operators over a real Hilbert space \(\mathcal{H }\). Without the condition that either \(\mathcal{H }\) is finite dimensional or the sum of \(n\) operators is maximal monotone, we prove that the sequence generated by the proposed method is strongly convergent to an extended solution for the problem, which is closest to the initial point. The main results presented in this paper generalize and improve some recent results in this topic.