ITERATIVE APPROXIMATIONS OF NULL POINTS OF UNIFORMLY ACCRETIVE OPERATORS WITH ESTIMATES OF THE CONVERGENCE RATE

TitleITERATIVE APPROXIMATIONS OF NULL POINTS OF UNIFORMLY ACCRETIVE OPERATORS WITH ESTIMATES OF THE CONVERGENCE RATE
Publication TypeJournal Article
Year of Publication2002
AuthorsAlber, Y, Reich, S, Shoikhet, D
Volume6
Issue1
Start Page89
Pagination16
Date Published2002
ISSN1083-2564
AMS47H06, 47H17, 65J15
Abstract

In this paper we study the implicit scheme $${ x_n = x_{n−1} − α_nx′_n , \ x′_n \ ∈ \ Ax_n, \ \  n = 1, 2, ...,}$$ where ${ A : D → X }$is a uniformly accretive set-valued operator satisfying the range condition and ${D}$ is a closed subset of a Banach space ${X}$. We present, in particular, a convergence theorem with estimates of the convergence rate and establish the stability of the method with respect to perturbations of the operator ${A}$. A result on the asymptotic behavior of the resolvents of ${A}$ is also included.

URLhttps://www.acadsol.eu/en/articles/6/1/7.pdf
Refereed DesignationRefereed
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