Strong convergence theorems for asymptotically relatively nonexpansive mappings with application

Shih Sen Chang; Xiong Rui Wang; Heung Wing Joseph Lee; Chi Kin Chan

Strong convergence theorems for asymptotically relatively nonexpansive mappings with application

Shih Sen Chang, Xiong Rui Wang, Heung Wing Joseph Lee, Chi Kin Chan

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

Abstract

The purpose of this paper is by using the hybrid iterative algorithm to prove some strong convergence theorems for two countable families of closed and asymptotically relatively nonexpansive mappings in Banach space. The results presented in the paper improve and extend the corresponding results of Su, Xu, Zhang [Nonlinear Anal., 73 (2010), 38903906.], Li, Huang, O'Regan [Comp. Math. Appl. 60 (2010), 1322-1331], Chang, Lee, Chan [Nonlinear Anal. 73 (2010), 2260-2270], Kang, Su, Zhang [Nonlinear Anal. HS (2010), doi:10.1016/j.nahs.2010. 05.002], Matsushita and Takahashi [J. Approx. Theory, 134 (2005), 257-266], Tan et al [Opuscula Math., 30:3 (2010), 341-348], Takahashia and Zembayashi [Nonlinear Anal, 70 (2009), 45-57] and Wattanawitoon, P. Kumam [Nonlinear Anal. Hybrid Systems, 3 (2009), 11-20] and others.

Original language	English
Pages (from-to)	45-60
Number of pages	16
Journal	Communications on Applied Nonlinear Analysis
Volume	18
Issue number	1
Publication status	Published - 1 Jan 2011

Keywords

Asymptotically relatively nonexpansive mapping
Generalized projection
Quasi-ø-nonexpansive mapping
Relatively nonexpansive mapping
Weak relatively nonexpansive mapping

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

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title = "Strong convergence theorems for asymptotically relatively nonexpansive mappings with application",

abstract = "The purpose of this paper is by using the hybrid iterative algorithm to prove some strong convergence theorems for two countable families of closed and asymptotically relatively nonexpansive mappings in Banach space. The results presented in the paper improve and extend the corresponding results of Su, Xu, Zhang [Nonlinear Anal., 73 (2010), 38903906.], Li, Huang, O'Regan [Comp. Math. Appl. 60 (2010), 1322-1331], Chang, Lee, Chan [Nonlinear Anal. 73 (2010), 2260-2270], Kang, Su, Zhang [Nonlinear Anal. HS (2010), doi:10.1016/j.nahs.2010. 05.002], Matsushita and Takahashi [J. Approx. Theory, 134 (2005), 257-266], Tan et al [Opuscula Math., 30:3 (2010), 341-348], Takahashia and Zembayashi [Nonlinear Anal, 70 (2009), 45-57] and Wattanawitoon, P. Kumam [Nonlinear Anal. Hybrid Systems, 3 (2009), 11-20] and others.",

keywords = "Asymptotically relatively nonexpansive mapping, Generalized projection, Quasi-{\o}-nonexpansive mapping, Relatively nonexpansive mapping, Weak relatively nonexpansive mapping",

author = "Chang, {Shih Sen} and Wang, {Xiong Rui} and Lee, {Heung Wing Joseph} and Chan, {Chi Kin}",

year = "2011",

month = jan,

day = "1",

language = "English",

volume = "18",

pages = "45--60",

journal = "Communications on Applied Nonlinear Analysis",

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AU - Chang, Shih Sen

AU - Wang, Xiong Rui

AU - Lee, Heung Wing Joseph

AU - Chan, Chi Kin

PY - 2011/1/1

Y1 - 2011/1/1

N2 - The purpose of this paper is by using the hybrid iterative algorithm to prove some strong convergence theorems for two countable families of closed and asymptotically relatively nonexpansive mappings in Banach space. The results presented in the paper improve and extend the corresponding results of Su, Xu, Zhang [Nonlinear Anal., 73 (2010), 38903906.], Li, Huang, O'Regan [Comp. Math. Appl. 60 (2010), 1322-1331], Chang, Lee, Chan [Nonlinear Anal. 73 (2010), 2260-2270], Kang, Su, Zhang [Nonlinear Anal. HS (2010), doi:10.1016/j.nahs.2010. 05.002], Matsushita and Takahashi [J. Approx. Theory, 134 (2005), 257-266], Tan et al [Opuscula Math., 30:3 (2010), 341-348], Takahashia and Zembayashi [Nonlinear Anal, 70 (2009), 45-57] and Wattanawitoon, P. Kumam [Nonlinear Anal. Hybrid Systems, 3 (2009), 11-20] and others.

AB - The purpose of this paper is by using the hybrid iterative algorithm to prove some strong convergence theorems for two countable families of closed and asymptotically relatively nonexpansive mappings in Banach space. The results presented in the paper improve and extend the corresponding results of Su, Xu, Zhang [Nonlinear Anal., 73 (2010), 38903906.], Li, Huang, O'Regan [Comp. Math. Appl. 60 (2010), 1322-1331], Chang, Lee, Chan [Nonlinear Anal. 73 (2010), 2260-2270], Kang, Su, Zhang [Nonlinear Anal. HS (2010), doi:10.1016/j.nahs.2010. 05.002], Matsushita and Takahashi [J. Approx. Theory, 134 (2005), 257-266], Tan et al [Opuscula Math., 30:3 (2010), 341-348], Takahashia and Zembayashi [Nonlinear Anal, 70 (2009), 45-57] and Wattanawitoon, P. Kumam [Nonlinear Anal. Hybrid Systems, 3 (2009), 11-20] and others.

KW - Asymptotically relatively nonexpansive mapping

KW - Generalized projection

KW - Quasi-ø-nonexpansive mapping

KW - Relatively nonexpansive mapping

KW - Weak relatively nonexpansive mapping

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M3 - Journal article

SN - 1074-133X

VL - 18

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EP - 60

JO - Communications on Applied Nonlinear Analysis

JF - Communications on Applied Nonlinear Analysis

IS - 1

ER -

Strong convergence theorems for asymptotically relatively nonexpansive mappings with application

Abstract

Keywords

ASJC Scopus subject areas

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