Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings
The purpose of this article is to present a general viscosity iteration process {xn} which defined by xn+1=(I-αnA)Txn+βnγf(xn)+(αn-βn)xn and to study the convergence of {xn}, where T is a nonexpansive mapping and A is a strongly positive linear operator, if {αn}, {βn} satisfy appropriate conditions,...
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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/10.1155/2012/605389 |
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| author | Yongfu Su |
| author_facet | Yongfu Su |
| author_sort | Yongfu Su |
| collection | DOAJ |
| description | The purpose of this article is to present a general viscosity iteration process {xn} which defined by xn+1=(I-αnA)Txn+βnγf(xn)+(αn-βn)xn and to study the convergence of {xn}, where T is a nonexpansive mapping and A is a strongly positive linear operator, if {αn}, {βn} satisfy appropriate conditions, then iteration sequence {xn} converges strongly to the unique solution x*∈f(T) of variational inequality 〈(A−γf)x*,x−x*〉≥0, for all x∈f(T). Meanwhile, a approximate iteration algorithm is presented which is used to calculate the fixed point of nonexpansive mapping and solution of variational inequality, the error estimate is also given. The results presented in this paper extend, generalize, and improve the results of Xu, G. Marino and Xu and some others. |
| format | Article |
| id | doaj-art-f9e8305448bc405d8ee06022554d602a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f9e8305448bc405d8ee06022554d602a2025-02-03T01:20:42ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/605389605389Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive MappingsYongfu Su0Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaThe purpose of this article is to present a general viscosity iteration process {xn} which defined by xn+1=(I-αnA)Txn+βnγf(xn)+(αn-βn)xn and to study the convergence of {xn}, where T is a nonexpansive mapping and A is a strongly positive linear operator, if {αn}, {βn} satisfy appropriate conditions, then iteration sequence {xn} converges strongly to the unique solution x*∈f(T) of variational inequality 〈(A−γf)x*,x−x*〉≥0, for all x∈f(T). Meanwhile, a approximate iteration algorithm is presented which is used to calculate the fixed point of nonexpansive mapping and solution of variational inequality, the error estimate is also given. The results presented in this paper extend, generalize, and improve the results of Xu, G. Marino and Xu and some others.http://dx.doi.org/10.1155/2012/605389 |
| spellingShingle | Yongfu Su Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings Abstract and Applied Analysis |
| title | Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings |
| title_full | Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings |
| title_fullStr | Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings |
| title_full_unstemmed | Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings |
| title_short | Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings |
| title_sort | approximate iteration algorithm with error estimate for fixed point of nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2012/605389 |
| work_keys_str_mv | AT yongfusu approximateiterationalgorithmwitherrorestimateforfixedpointofnonexpansivemappings |