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- Title
APPROXIMATING FIXED POINTS OF THE COMPOSITION OF TWO RESOLVENT OPERATORS.
- Authors
BOIKANYO, OGANEDITSE A.
- Abstract
Let A and B be maximal monotone operators de_ned on a real Hilbert space H, and let Fix(JµA JµB) ≠ φ, where JµA y := (I + µA)-1y 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 (xn) generated by the iterative method xn+1 = JµAyn, with yn = JµBxn converges weakly to some point in Fix(JµA JµB). In this paper, we show that the modi_ed 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(JµA JµB) and Fix(JµB JµA).
- Subjects
FIXED point theory; RESOLVENTS (Mathematics); MONOTONE operators
- Publication
Fixed Point Theory, 2017, Vol 18, Issue 1, p137
- ISSN
1583-5022
- Publication type
Article
- DOI
10.24193/fpt-ro.2017.1.11