Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces
Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, ℱ={T(h):h≥0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f:K→K a fixed contractive mapping with contractive coefficient β∈(0,1). We...
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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/10.1155/2008/687815 |
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| author | Yali Li Jianjun Liu Lei Deng |
| author_facet | Yali Li Jianjun Liu Lei Deng |
| author_sort | Yali Li |
| collection | DOAJ |
| description | Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, ℱ={T(h):h≥0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f:K→K a fixed contractive mapping with contractive coefficient β∈(0,1). We prove that the following implicit and modified implicit viscosity iterative schemes {xn} defined by xn=αnf(xn)+(1−αn)T(tn)xn and xn=αnyn+(1−αn)T(tn)xn, yn=βnf(xn−1)+(1−βn)xn−1 strongly converge to p∈F as n→∞ and p is the unique solution to the following variational inequality: 〈f(p)−p,j(y−p)〉≤0 for all y∈F. |
| format | Article |
| id | doaj-art-e1b8d853ef1a41b587811ca2b1c5550e |
| 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-e1b8d853ef1a41b587811ca2b1c5550e2025-02-03T01:28:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/687815687815Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach SpacesYali Li0Jianjun Liu1Lei Deng2School 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 K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, ℱ={T(h):h≥0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f:K→K a fixed contractive mapping with contractive coefficient β∈(0,1). We prove that the following implicit and modified implicit viscosity iterative schemes {xn} defined by xn=αnf(xn)+(1−αn)T(tn)xn and xn=αnyn+(1−αn)T(tn)xn, yn=βnf(xn−1)+(1−βn)xn−1 strongly converge to p∈F as n→∞ and p is the unique solution to the following variational inequality: 〈f(p)−p,j(y−p)〉≤0 for all y∈F.http://dx.doi.org/10.1155/2008/687815 |
| spellingShingle | Yali Li Jianjun Liu Lei Deng Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces |
| title_full | Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces |
| title_fullStr | Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces |
| title_full_unstemmed | Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces |
| title_short | Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces |
| title_sort | convergence to common fixed point for generalized asymptotically nonexpansive semigroup in banach spaces |
| url | http://dx.doi.org/10.1155/2008/687815 |
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