Three Convergence Results for Inexact Iterates of Uniformly Locally Nonexpansive Mappings

Author:

Reich Simeon1ORCID,Zaslavski Alexander J.1

Affiliation:

1. Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel

Abstract

In 2006, together with D. Butnariu, we showed that if all iterates of a nonexpansive self-mapping of a complete metric space converge, then all its inexact iterates with summable computational errors converge too. In a recent paper of ours, we have extended this result to uniformly locally nonexpansive self-mappings of a complete metric space. In the present paper, we establish analogous results for uniformly locally nonexpansive mappings which take a nonempty closed subset of a complete metric space into the space. In the particular case of a Banach space, if the operator is symmetric, then the set of all limit points of its iterates is also symmetric.

Funder

Israel Science Foundation

Fund for the Promotion of Research at the Technion

Technion General Research Fund

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Reference24 articles.

1. Fixed points for nonexpansive mappings and generalized nonexpansive mappings on Banach lattices;Pure Appl. Func. Anal.,2016

2. Strong and weak convergence theorems for locally nonexpansive mappings in Banach spaces;Bruck;Nonlinear Anal.,1982

3. Butnariu, D., Reich, S., and Zaslavski, A.J. (2006). Fixed Point Theory and Its Applications, Yokohama Publishers.

4. Sur la convergence des approximations successives pour les contractions non linéaires dans un espace de Banach;Myjak;C. R. Acad. Sci. Paris,1976

5. Goebel, K., and Kirk, W.A. (1990). Topics in Metric Fixed Point Theory, Cambridge University Press.

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