Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups. (2nd April 2013)

• Record Type: Journal Article
• Authors: Zhu, Li-Jun
• Other Names: Yao Jen-Chih Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-04-02
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/604369
• Languages: English
• ISSNs: 1085-3375

Abstract

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 - γ f ) x * - ( I - B ) S x *, 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.