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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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |