Strong convergence theorems of total quasi-φ-asymptotically nonexpansive semi-groups in Banach spaces

Shih Sen Chang; Chi Kin Chan; Li Yang; Xiong Rui Wang

doi:10.1016/j.amc.2013.08.058

Strong convergence theorems of total quasi-φ-asymptotically nonexpansive semi-groups in Banach spaces

Shih Sen Chang
, Chi Kin Chan
, Li Yang
, Xiong Rui Wang

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

1 Citation (Scopus)

Abstract

The purpose of this article is first to introduce the concept of total quasi-φ-asymptotically nonexpansive semigroups which contains many kinds of semi-groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for this kind of semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results announced by many authors.

Original language	English
Pages (from-to)	398-404
Number of pages	7
Journal	Applied Mathematics and Computation
Volume	224
DOIs	https://doi.org/10.1016/j.amc.2013.08.058
Publication status	Published - 4 Oct 2013

Keywords

Generalized projection
Modified Halpern-Mann-type iteration
Quasi-φ-nonexpansive semi-groups
Quasi-φ-symptotically nonexpansive semi-groups
Relatively nonexpansive semi-groups
Total quasi-φ-symptotically nonexpansive semi-groups

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2013.08.058

Cite this

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title = "Strong convergence theorems of total quasi-φ-asymptotically nonexpansive semi-groups in Banach spaces",

abstract = "The purpose of this article is first to introduce the concept of total quasi-φ-asymptotically nonexpansive semigroups which contains many kinds of semi-groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for this kind of semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results announced by many authors.",

keywords = "Generalized projection, Modified Halpern-Mann-type iteration, Quasi-φ-nonexpansive semi-groups, Quasi-φ-symptotically nonexpansive semi-groups, Relatively nonexpansive semi-groups, Total quasi-φ-symptotically nonexpansive semi-groups",

author = "Chang, \{Shih Sen\} and Chan, \{Chi Kin\} and Li Yang and Wang, \{Xiong Rui\}",

year = "2013",

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doi = "10.1016/j.amc.2013.08.058",

language = "English",

volume = "224",

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journal = "Applied Mathematics and Computation",

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AU - Chang, Shih Sen

AU - Chan, Chi Kin

AU - Yang, Li

AU - Wang, Xiong Rui

PY - 2013/10/4

Y1 - 2013/10/4

N2 - The purpose of this article is first to introduce the concept of total quasi-φ-asymptotically nonexpansive semigroups which contains many kinds of semi-groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for this kind of semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results announced by many authors.

AB - The purpose of this article is first to introduce the concept of total quasi-φ-asymptotically nonexpansive semigroups which contains many kinds of semi-groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for this kind of semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results announced by many authors.

KW - Generalized projection

KW - Modified Halpern-Mann-type iteration

KW - Quasi-φ-nonexpansive semi-groups

KW - Quasi-φ-symptotically nonexpansive semi-groups

KW - Relatively nonexpansive semi-groups

KW - Total quasi-φ-symptotically nonexpansive semi-groups

UR - https://www.scopus.com/pages/publications/84884807015

U2 - 10.1016/j.amc.2013.08.058

DO - 10.1016/j.amc.2013.08.058

M3 - Journal article

SN - 0096-3003

VL - 224

SP - 398

EP - 404

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Strong convergence theorems of total quasi-φ-asymptotically nonexpansive semi-groups in Banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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