Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space
Let C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup ℑ={T(s):s≥0} with a common fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient γ¯>0. Let 0<γ<Î...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2008-11-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/484050 |
| _version_ | 1818568904034746368 |
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| author | Yongfu Su Suhong Li Lihua Li |
| author_facet | Yongfu Su Suhong Li Lihua Li |
| author_sort | Yongfu Su |
| collection | DOAJ |
| description | Let C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup ℑ={T(s):s≥0} with a common fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient γ¯>0. Let 0<γ<γ¯/α. It is proved that the sequence {xn} generated iteratively by xn=(I−αnA)(1/tn)∫0tnT(s)ynds+αnγf(xn),yn=(I−βnA)xn+βnγf(xn) converges strongly to a common fixed point x∗∈F(ℑ) which solves the variational inequality 〈(γf−A)x∗,z−x∗〉≤0 for all z∈F(ℑ). |
| first_indexed | 2024-12-14T06:41:10Z |
| format | Article |
| id | doaj.art-a674fc5698b4465ab41e58de9536905b |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-14T06:41:10Z |
| publishDate | 2008-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-a674fc5698b4465ab41e58de9536905b2022-12-21T23:13:14ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122008-11-01200810.1155/2008/484050Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert SpaceYongfu SuSuhong LiLihua LiLet C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup ℑ={T(s):s≥0} with a common fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient γ¯>0. Let 0<γ<γ¯/α. It is proved that the sequence {xn} generated iteratively by xn=(I−αnA)(1/tn)∫0tnT(s)ynds+αnγf(xn),yn=(I−βnA)xn+βnγf(xn) converges strongly to a common fixed point x∗∈F(ℑ) which solves the variational inequality 〈(γf−A)x∗,z−x∗〉≤0 for all z∈F(ℑ).http://dx.doi.org/10.1155/2008/484050 |
| spellingShingle | Yongfu Su Suhong Li Lihua Li Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space Fixed Point Theory and Applications |
| title | Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space |
| title_full | Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space |
| title_fullStr | Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space |
| title_full_unstemmed | Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space |
| title_short | Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space |
| title_sort | composite implicit general iterative process for a nonexpansive semigroup in hilbert space |
| url | http://dx.doi.org/10.1155/2008/484050 |
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