Approximating fixed points of the composition of two resolvent operators

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).
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APA

Oganeditse, B (2024). Approximating fixed points of the composition of two resolvent operators. Afribary. Retrieved from https://afribary.com/works/approximating-fixed-points-of-the-composition-of-two-resolvent-operators

MLA 8th

Oganeditse, Boikanyo "Approximating fixed points of the composition of two resolvent operators" Afribary. Afribary, 30 Mar. 2024, https://afribary.com/works/approximating-fixed-points-of-the-composition-of-two-resolvent-operators. Accessed 28 May. 2024.

MLA7

Oganeditse, Boikanyo . "Approximating fixed points of the composition of two resolvent operators". Afribary, Afribary, 30 Mar. 2024. Web. 28 May. 2024. < https://afribary.com/works/approximating-fixed-points-of-the-composition-of-two-resolvent-operators >.

Chicago

Oganeditse, Boikanyo . "Approximating fixed points of the composition of two resolvent operators" Afribary (2024). Accessed May 28, 2024. https://afribary.com/works/approximating-fixed-points-of-the-composition-of-two-resolvent-operators