General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities
This paper deals with new methods for approximating a solution to the fixed point problem; find x̃∈F(T), where H is a Hilbert space, C is a closed convex subset of H, f is a ρ-contraction from C into H, 0<ρ<1, A is a strongly positive linear-bounded operator with coefficient γ̅>0, 0<γ<...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/174318 |
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| author | Nopparat Wairojjana Poom Kumam |
| author_facet | Nopparat Wairojjana Poom Kumam |
| author_sort | Nopparat Wairojjana |
| collection | DOAJ |
| description | This paper deals with new methods for approximating a solution to the fixed point problem; find x̃∈F(T), where H is a Hilbert space, C is a closed convex subset of H, f is a ρ-contraction from C into H, 0<ρ<1, A is a strongly positive linear-bounded operator with coefficient γ̅>0, 0<γ<γ̅/ρ, T is a nonexpansive mapping on C, and PF(T) denotes the metric projection on the set of fixed point of T. Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality 〈(A-γf)x̃+τ(I-S)x̃,x-x̃〉≥0 for x∈F(T), where τ∈[0,∞). Our results generalize and improve the corresponding results of Yao et al. (2010) and some authors. Furthermore, we give an example which supports our main theorem in the last part. |
| format | Article |
| id | doaj-art-2bd66bd390944cd8bb4aee6f6e8cd076 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2bd66bd390944cd8bb4aee6f6e8cd0762025-02-03T06:42:17ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/174318174318General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational InequalitiesNopparat Wairojjana0Poom Kumam1Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandThis paper deals with new methods for approximating a solution to the fixed point problem; find x̃∈F(T), where H is a Hilbert space, C is a closed convex subset of H, f is a ρ-contraction from C into H, 0<ρ<1, A is a strongly positive linear-bounded operator with coefficient γ̅>0, 0<γ<γ̅/ρ, T is a nonexpansive mapping on C, and PF(T) denotes the metric projection on the set of fixed point of T. Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality 〈(A-γf)x̃+τ(I-S)x̃,x-x̃〉≥0 for x∈F(T), where τ∈[0,∞). Our results generalize and improve the corresponding results of Yao et al. (2010) and some authors. Furthermore, we give an example which supports our main theorem in the last part.http://dx.doi.org/10.1155/2012/174318 |
| spellingShingle | Nopparat Wairojjana Poom Kumam General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities Journal of Applied Mathematics |
| title | General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities |
| title_full | General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities |
| title_fullStr | General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities |
| title_full_unstemmed | General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities |
| title_short | General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities |
| title_sort | general iterative algorithms for hierarchical fixed points approach to variational inequalities |
| url | http://dx.doi.org/10.1155/2012/174318 |
| work_keys_str_mv | AT nopparatwairojjana generaliterativealgorithmsforhierarchicalfixedpointsapproachtovariationalinequalities AT poomkumam generaliterativealgorithmsforhierarchicalfixedpointsapproachtovariationalinequalities |