Abstract
In our recent paper we obtained an extension of a theorem of Tam (2018), which was established for iterates of a set-valued paracontracting operators in a finite-dimensional Euclidean space. This extension was obtained for exact iterates of maps in a metric space. In the present paper we prove two analogs of this result for inexact iterates under the presence of computational errors. In the first result, the errors are summable, while for the second one they converge to zero. In a particular case of a Banach space, if all the operators are symmetric, then the set of all limit points of iterates is symmetric too.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference32 articles.
1. An unifying approach for some nonexpansiveness conditions on modular vector spaces;Bejenaru;Nonlinear Anal. Model. Control,2020
2. Fixed points for nonexpansive mappings and generalized nonexpansive mappings on Banach lattices;Pure Appl. Func. Anal.,2016
3. Sur la convergence des approximations successives pour les contractions non linéaires dans un espace de Banach;Myjak;Comptes Rendus Acad. Sci. Paris,1976
4. Generic existence and approximation of fixed points for nonexpansive set-valued maps;Myjak;Set-Valued Var. Anal.,2009
5. Goebel, K., and Kirk, W.A. (1990). Topics in Metric Fixed Point Theory, Cambridge University Press.
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