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