Approximating fixed points of the composition of two resolvent operators

Research output: Contribution to journalArticle

Abstract

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 (xn) generated by the iterative method, (eqution found) converges weakly to some point in Fix(JAμ JBμ). 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 (JAμ JBμ) and Fix (JBμ JAμ).

Original languageEnglish
Pages (from-to)137-139
Number of pages3
JournalFixed Point Theory
Volume18
Issue number1
DOIs
Publication statusPublished - 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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