Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups
The purpose of the present paper is to study the hierarchical constrained variational inequalities of finding a point x* such that x*∈Ω,〈(A-γf)x*-(I-B)Sx*,x-x*〉≥0, ∀x∈Ω, where Ω is the set of the solutions of the following variational inequality: x*∈Ϝ,〈(A-S)x*,x-x*〉≥0, ∀x∈Ϝ, where A,B are two stro...
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| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/604369 |
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| author | Li-Jun Zhu |
| author_facet | Li-Jun Zhu |
| author_sort | Li-Jun Zhu |
| collection | DOAJ |
| description | The purpose of the present paper is to study the hierarchical constrained variational inequalities of finding a point x* such that x*∈Ω,〈(A-γf)x*-(I-B)Sx*,x-x*〉≥0, ∀x∈Ω, where Ω is the set of the solutions of the following variational inequality: x*∈Ϝ,〈(A-S)x*,x-x*〉≥0, ∀x∈Ϝ, where A,B are two strongly positive bounded linear operators, f is a ρ-contraction, S is a nonexpansive mapping, and Ϝ is the fixed points set of a nonexpansive semigroup {T(s)}s≥0. We present a double-net convergence hierarchical to some elements in Ϝ which solves the above hierarchical constrained variational inequalities. |
| format | Article |
| id | doaj-art-a96e98a5fbff4fe2b8c6081006c6cb88 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a96e98a5fbff4fe2b8c6081006c6cb882025-02-03T01:09:35ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/604369604369Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive SemigroupsLi-Jun Zhu0School of Information and Calculation, Beifang University of Nationalities, Yinchuan 750021, ChinaThe purpose of the present paper is to study the hierarchical constrained variational inequalities of finding a point x* such that x*∈Ω,〈(A-γf)x*-(I-B)Sx*,x-x*〉≥0, ∀x∈Ω, where Ω is the set of the solutions of the following variational inequality: x*∈Ϝ,〈(A-S)x*,x-x*〉≥0, ∀x∈Ϝ, where A,B are two strongly positive bounded linear operators, f is a ρ-contraction, S is a nonexpansive mapping, and Ϝ is the fixed points set of a nonexpansive semigroup {T(s)}s≥0. We present a double-net convergence hierarchical to some elements in Ϝ which solves the above hierarchical constrained variational inequalities.http://dx.doi.org/10.1155/2013/604369 |
| spellingShingle | Li-Jun Zhu Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups Abstract and Applied Analysis |
| title | Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups |
| title_full | Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups |
| title_fullStr | Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups |
| title_full_unstemmed | Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups |
| title_short | Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups |
| title_sort | approximation for the hierarchical constrained variational inequalities over the fixed points of nonexpansive semigroups |
| url | http://dx.doi.org/10.1155/2013/604369 |
| work_keys_str_mv | AT lijunzhu approximationforthehierarchicalconstrainedvariationalinequalitiesoverthefixedpointsofnonexpansivesemigroups |