Approximating fixed points of nonexpansive mappings
We consider a mapping S of the form S=α0I+α1T1+α2T2+⋯+αkTk, where αi≥0, α0>0, α1>0 and ∑i=0kαi=1. We show that the Picard iterates of S converge to a common fixed point of Ti(i=1,2,…,k)in a Banach space when Ti(i=1,2,…,k) are nonexpansive.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200003252 |
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| _version_ | 1850164213880717312 |
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| author | Guimei Liu Deng Lei Shenghong Li |
| author_facet | Guimei Liu Deng Lei Shenghong Li |
| author_sort | Guimei Liu |
| collection | DOAJ |
| description | We consider a mapping S of the form
S=α0I+α1T1+α2T2+⋯+αkTk,
where αi≥0, α0>0, α1>0 and
∑i=0kαi=1. We show that the Picard iterates of
S converge to a common fixed point of Ti(i=1,2,…,k)in a Banach space when Ti(i=1,2,…,k) are
nonexpansive. |
| format | Article |
| id | doaj-art-eaac4857e1254bf883efef76e65ccff8 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-eaac4857e1254bf883efef76e65ccff82025-08-20T02:22:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124317317710.1155/S0161171200003252Approximating fixed points of nonexpansive mappingsGuimei Liu0Deng Lei1Shenghong Li2Department of Mathematics, Zhejiang University, Zhejiang, 310027, ChinaDepartment of Mathematics, Southwest China Normal University, Beibei, Chongqing 400715, ChinaDepartment of Mathematics, Zhejiang University, Zhejiang, 310027, ChinaWe consider a mapping S of the form S=α0I+α1T1+α2T2+⋯+αkTk, where αi≥0, α0>0, α1>0 and ∑i=0kαi=1. We show that the Picard iterates of S converge to a common fixed point of Ti(i=1,2,…,k)in a Banach space when Ti(i=1,2,…,k) are nonexpansive.http://dx.doi.org/10.1155/S0161171200003252Fixed pointnonexpansive mappingiterative process. |
| spellingShingle | Guimei Liu Deng Lei Shenghong Li Approximating fixed points of nonexpansive mappings International Journal of Mathematics and Mathematical Sciences Fixed point nonexpansive mapping iterative process. |
| title | Approximating fixed points of nonexpansive mappings |
| title_full | Approximating fixed points of nonexpansive mappings |
| title_fullStr | Approximating fixed points of nonexpansive mappings |
| title_full_unstemmed | Approximating fixed points of nonexpansive mappings |
| title_short | Approximating fixed points of nonexpansive mappings |
| title_sort | approximating fixed points of nonexpansive mappings |
| topic | Fixed point nonexpansive mapping iterative process. |
| url | http://dx.doi.org/10.1155/S0161171200003252 |
| work_keys_str_mv | AT guimeiliu approximatingfixedpointsofnonexpansivemappings AT denglei approximatingfixedpointsofnonexpansivemappings AT shenghongli approximatingfixedpointsofnonexpansivemappings |