Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators
An iteration process studied by Chidume and Zegeye 2002 is proved to converge strongly to a solution of the equation Au=0 where A is a bounded m-accretive operator on certain real Banach spaces E that include Lp spaces 2≤p<∞. The iteration process does not involve the computation of the resolvent...
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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/10.1155/2012/681348 |
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| author | C. E. Chidume N. Djitté |
| author_facet | C. E. Chidume N. Djitté |
| author_sort | C. E. Chidume |
| collection | DOAJ |
| description | An iteration process studied by Chidume and Zegeye 2002 is proved to converge strongly to a solution of the equation Au=0 where A is a bounded m-accretive operator on certain real Banach spaces E that include Lp spaces 2≤p<∞. The iteration process does not involve the computation of the resolvent at any step of the process and does not involve the projection of an initial vector onto the intersection of two convex subsets of E, setbacks associated with the classical proximal point algorithm of Martinet 1970, Rockafellar 1976 and its modifications by various authors for approximating of a solution of this equation. The ideas of the iteration process are applied to approximate fixed points of uniformly continuous pseudocontractive maps. |
| format | Article |
| id | doaj-art-2ac9888a971f40fdb3ffa4e6989c157a |
| 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-2ac9888a971f40fdb3ffa4e6989c157a2025-02-03T07:25:46ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/681348681348Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear OperatorsC. E. Chidume0N. Djitté1Mathematics Institute, African University of Science and Technology, Abuja, NigeriaMathematics Institute, African University of Science and Technology, Abuja, NigeriaAn iteration process studied by Chidume and Zegeye 2002 is proved to converge strongly to a solution of the equation Au=0 where A is a bounded m-accretive operator on certain real Banach spaces E that include Lp spaces 2≤p<∞. The iteration process does not involve the computation of the resolvent at any step of the process and does not involve the projection of an initial vector onto the intersection of two convex subsets of E, setbacks associated with the classical proximal point algorithm of Martinet 1970, Rockafellar 1976 and its modifications by various authors for approximating of a solution of this equation. The ideas of the iteration process are applied to approximate fixed points of uniformly continuous pseudocontractive maps.http://dx.doi.org/10.1155/2012/681348 |
| spellingShingle | C. E. Chidume N. Djitté Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators Abstract and Applied Analysis |
| title | Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators |
| title_full | Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators |
| title_fullStr | Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators |
| title_full_unstemmed | Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators |
| title_short | Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators |
| title_sort | strong convergence theorems for zeros of bounded maximal monotone nonlinear operators |
| url | http://dx.doi.org/10.1155/2012/681348 |
| work_keys_str_mv | AT cechidume strongconvergencetheoremsforzerosofboundedmaximalmonotonenonlinearoperators AT ndjitte strongconvergencetheoremsforzerosofboundedmaximalmonotonenonlinearoperators |