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(J(mu)(A) J(mu)(B)) not equal empty set, where J(mu)(A) (I + mu A)(-1)y and mu 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 x(n+1) = J(mu)(A)y(n), with y(n) = J(mu)(B)x(n) converges weakly to some point in Fix(J(mu)(A)J(mu)(B)). 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(mu)(A)J(mu)(B)) and Fix(J(mu)(B)J(mu)(A)).