Approximating fixed points of the composition of two resolvent operators

Let A and B be maximal monotone operators defined on a real Hilbert space H, and let Fix, (eqution found) and μ is a given positive number. [H. H. Bauschke, P. L. Combettes and S. Reich, The asymptotic behavior of the composition of two resolvents, Nonlinear Anal. 60 (2005), no. 2, 283-301] proved that any sequence (x_n) generated by the iterative method, (eqution found) converges weakly to some point in Fix(J^A_μ J^B_μ). In this paper, we show that the modified method of alternating resolvents introduced in [O. A. Boikanyo, A proximal point method involving two resolvent operators, Abstr. Appl. Anal. 2012, Article ID 892980, (2012)] produces sequences that converge strongly to some points in Fix (J^A_μ J^B_μ) and Fix (J^B_μ J^A_μ).