Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces
Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite famil...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/926078 |
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| author | Yan Tang |
| author_facet | Yan Tang |
| author_sort | Yan Tang |
| collection | DOAJ |
| description | Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings. |
| format | Article |
| id | doaj-art-1e2740cd8d7546de9cc756799d8d6465 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1e2740cd8d7546de9cc756799d8d64652025-02-03T06:06:56ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/926078926078Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach SpacesYan Tang0College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaSuppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.http://dx.doi.org/10.1155/2013/926078 |
| spellingShingle | Yan Tang Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces Journal of Applied Mathematics |
| title | Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces |
| title_full | Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces |
| title_fullStr | Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces |
| title_full_unstemmed | Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces |
| title_short | Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces |
| title_sort | viscosity approximation methods and strong convergence theorems for the fixed point of pseudocontractive and monotone mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2013/926078 |
| work_keys_str_mv | AT yantang viscosityapproximationmethodsandstrongconvergencetheoremsforthefixedpointofpseudocontractiveandmonotonemappingsinbanachspaces |