Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups

Li-Jun Zhu

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/604369

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:604369

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