Generic power convergence of operators in Banach spaces

Dan Butnariu; Simeon Reich; Alexander J. Zaslavski

doi:10.1080/01630569908816915

Generic power convergence of operators in Banach spaces

Dan Butnariu, Simeon Reich, Alexander 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. We consider complete metric spaces of self-mappings of K which are nonexpansive with respect, to a convex function on X. We prove that the iterates of a generic operator in these spaces converge strongly. In some cases the limits do not depend on the initial points and are the unique fixed point of the operator.

Original language	English
Pages (from-to)	629-650
Number of pages	22
Journal	Numerical Functional Analysis and Optimization
Volume	20
Issue number	7
DOIs	https://doi.org/10.1080/01630569908816915
State	Published - 1999

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

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abstract = "Let K be a closed convex subset of a Banach space X. We consider complete metric spaces of self-mappings of K which are nonexpansive with respect, to a convex function on X. We prove that the iterates of a generic operator in these spaces converge strongly. In some cases the limits do not depend on the initial points and are the unique fixed point of the operator.",

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AU - Zaslavski, Alexander J.

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AB - Let K be a closed convex subset of a Banach space X. We consider complete metric spaces of self-mappings of K which are nonexpansive with respect, to a convex function on X. We prove that the iterates of a generic operator in these spaces converge strongly. In some cases the limits do not depend on the initial points and are the unique fixed point of the operator.

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DO - 10.1080/01630569908816915

M3 - Article

AN - SCOPUS:0032594392

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JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 7

ER -

Generic power convergence of operators in Banach spaces

Abstract

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