Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions
This paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces by yn=βnSxn+(1-βn)xn, xn+1=PC[αnf(xn)+(1-αn)∑i=1∞μi(n)Tiyn], and ∀n≥0, where Ti:C↦H is a nonself ki-strictly pseudocontraction. Under certain ap...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/457024 |
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| _version_ | 1849694645806694400 |
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| author | Wei Xu Yuanheng Wang |
| author_facet | Wei Xu Yuanheng Wang |
| author_sort | Wei Xu |
| collection | DOAJ |
| description | This paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces by yn=βnSxn+(1-βn)xn, xn+1=PC[αnf(xn)+(1-αn)∑i=1∞μi(n)Tiyn], and ∀n≥0, where Ti:C↦H is a nonself ki-strictly pseudocontraction. Under certain approximate conditions, the sequence {xn} converges strongly to x*∈⋂i=1∞F(Ti), which solves some variational inequality. The results here improve and extend some recent results. |
| format | Article |
| id | doaj-art-f3bdb2364d6a4fbda2d828dce9a04f2d |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f3bdb2364d6a4fbda2d828dce9a04f2d2025-08-20T03:20:00ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/457024457024Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself PseudocontractionsWei Xu0Yuanheng Wang1Tongji Zhejiang College, Zhejiang 314000, ChinaDepartment of Mathematics, Zhejiang Normal University, Zhejiang 321004, ChinaThis paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces by yn=βnSxn+(1-βn)xn, xn+1=PC[αnf(xn)+(1-αn)∑i=1∞μi(n)Tiyn], and ∀n≥0, where Ti:C↦H is a nonself ki-strictly pseudocontraction. Under certain approximate conditions, the sequence {xn} converges strongly to x*∈⋂i=1∞F(Ti), which solves some variational inequality. The results here improve and extend some recent results.http://dx.doi.org/10.1155/2012/457024 |
| spellingShingle | Wei Xu Yuanheng Wang Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions Abstract and Applied Analysis |
| title | Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions |
| title_full | Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions |
| title_fullStr | Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions |
| title_full_unstemmed | Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions |
| title_short | Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions |
| title_sort | strong convergence of the iterative methods for hierarchical fixed point problems of an infinite family of strictly nonself pseudocontractions |
| url | http://dx.doi.org/10.1155/2012/457024 |
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