Asymptotic behavior of relatively nonexpansive operators in banach spaces

D. Butnariu; S. Reich; A. J. Zaslavski

doi:10.1515/JAA.2001.151

Asymptotic behavior of relatively nonexpansive operators in banach spaces

D. Butnariu
, S. Reich
, A. J. Zaslavski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F.

Original language	English
Pages (from-to)	151-174
Number of pages	24
Journal	Journal of Applied Analysis
Volume	7
Issue number	2
DOIs	https://doi.org/10.1515/JAA.2001.151
State	Published - Dec 2001

Bibliographical note

Funding Information:
The work of the first two authors was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Grants 293/97 and 592/00). The second author was also partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund — E. and M. Mendelson Research Fund.

Keywords

Bregman distance
Convex function
Fixed point
Generic property
Iterative algorithm
Uniform space

ASJC Scopus subject areas

Mathematical Physics
Statistics, Probability and Uncertainty
Computational Theory and Mathematics
Applied Mathematics

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10.1515/JAA.2001.151

Cite this

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abstract = "Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F.",

keywords = "Bregman distance, Convex function, Fixed point, Generic property, Iterative algorithm, Uniform space",

author = "D. Butnariu and S. Reich and Zaslavski, \{A. J.\}",

note = "Funding Information: The work of the first two authors was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Grants 293/97 and 592/00). The second author was also partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund — E. and M. Mendelson Research Fund.",

year = "2001",

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doi = "10.1515/JAA.2001.151",

language = "English",

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AU - Butnariu, D.

AU - Reich, S.

AU - Zaslavski, A. J.

N1 - Funding Information: The work of the first two authors was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Grants 293/97 and 592/00). The second author was also partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund — E. and M. Mendelson Research Fund.

PY - 2001/12

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N2 - Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F.

AB - Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F.

KW - Bregman distance

KW - Convex function

KW - Fixed point

KW - Generic property

KW - Iterative algorithm

KW - Uniform space

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JF - Journal of Applied Analysis

IS - 2

ER -

Asymptotic behavior of relatively nonexpansive operators in banach spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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