Approximation of nearest common fixed point of nonexpansive mappings in hilbert spaces

Shi Sheng Zhang; Heung Wing Joseph Lee; Chi Kin Chan

doi:10.1007/s10114-005-0821-0

Approximation of nearest common fixed point of nonexpansive mappings in hilbert spaces

Shi Sheng Zhang, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publication › Journal article › Academic research › peer-review

2 Citations (Scopus)

Abstract

The purpose of this paper is to study the convergence problem of the iteration scheme xn+1= λn+1y+(1-λn+1) Tn+1xnfor a family of infinitely many nonexpansive mappings T1, T2, . . . in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.

Original language	English
Pages (from-to)	1889-1896
Number of pages	8
Journal	Acta Mathematica Sinica, English Series
Volume	23
Issue number	10
DOIs	https://doi.org/10.1007/s10114-005-0821-0
Publication status	Published - 1 Oct 2007

Keywords

Common fixed point
Family of nonexpansive mappings
Iterative scheme
Nearest point projection

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

More information

10.1007/s10114-005-0821-0

Cite this

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abstract = "The purpose of this paper is to study the convergence problem of the iteration scheme xn+1= λn+1y+(1-λn+1) Tn+1xnfor a family of infinitely many nonexpansive mappings T1, T2, . . . in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.",

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AU - Lee, Heung Wing Joseph

AU - Chan, Chi Kin

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Y1 - 2007/10/1

N2 - The purpose of this paper is to study the convergence problem of the iteration scheme xn+1= λn+1y+(1-λn+1) Tn+1xnfor a family of infinitely many nonexpansive mappings T1, T2, . . . in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.

AB - The purpose of this paper is to study the convergence problem of the iteration scheme xn+1= λn+1y+(1-λn+1) Tn+1xnfor a family of infinitely many nonexpansive mappings T1, T2, . . . in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.

KW - Common fixed point

KW - Family of nonexpansive mappings

KW - Iterative scheme

KW - Nearest point projection

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DO - 10.1007/s10114-005-0821-0

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JO - Acta Mathematica Sinica, English Series

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Approximation of nearest common fixed point of nonexpansive mappings in hilbert spaces

Abstract

Keywords

ASJC Scopus subject areas

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