Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space
Let C be a nonempty closed and convex subset of a Hilbert space H, let T and S:C→C be two commutative generalized asymptotically nonexpansive mappings. We introduce an implicit iteration process of S and T defined by xn=αnx0+(1−αn)(2/((n+1)(n+2)))∑k=0n∑i+j=kSiTjxn, and then prove that {xn} converges...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/649510 |
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| _version_ | 1832550737172758528 |
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| author | Lili He Lei Deng Jianjun Liu |
| author_facet | Lili He Lei Deng Jianjun Liu |
| author_sort | Lili He |
| collection | DOAJ |
| description | Let C be a nonempty closed and convex subset of a Hilbert space H, let T and S:C→C be two commutative generalized asymptotically nonexpansive mappings. We introduce an implicit iteration process of S and T defined by xn=αnx0+(1−αn)(2/((n+1)(n+2)))∑k=0n∑i+j=kSiTjxn, and then prove that {xn} converges strongly to a common fixed point of S and T. The results generalize and unify the corresponding results. |
| format | Article |
| id | doaj-art-f700987a14c246cfa979b9faa8ab8c0b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f700987a14c246cfa979b9faa8ab8c0b2025-02-03T06:06:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/649510649510Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert SpaceLili He0Lei Deng1Jianjun Liu2School of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaLet C be a nonempty closed and convex subset of a Hilbert space H, let T and S:C→C be two commutative generalized asymptotically nonexpansive mappings. We introduce an implicit iteration process of S and T defined by xn=αnx0+(1−αn)(2/((n+1)(n+2)))∑k=0n∑i+j=kSiTjxn, and then prove that {xn} converges strongly to a common fixed point of S and T. The results generalize and unify the corresponding results.http://dx.doi.org/10.1155/2008/649510 |
| spellingShingle | Lili He Lei Deng Jianjun Liu Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space International Journal of Mathematics and Mathematical Sciences |
| title | Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space |
| title_full | Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space |
| title_fullStr | Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space |
| title_full_unstemmed | Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space |
| title_short | Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space |
| title_sort | strong convergence theorem of implicit iteration process for generalized asymptotically nonexpansive mappings in hilbert space |
| url | http://dx.doi.org/10.1155/2008/649510 |
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