Regularized hybrid iterative algorithms for triple hierarchical variational inequalities.

In this paper, we introduce and study a triple hierarchical variational inequality (THVI) with constraints of minimization and equilibrium problems. More precisely, let Fix(T) be the fixed point set of a nonexpansive mapping, let MEP(Θ,ϕ) be the solution set of a mixed equilibrium problem (MEP), and let Γ be the solution set of a minimization problem (MP) for a convex and continuously Frechet differential functional in Hilbert spaces. We want to find a solution x* ∈ Fix(T) ∩ MEP(Θ,ϕ) ∩ Γ of a variational inequality with a variational inequality constraint over the intersection of Fix(T), MEP(Θ,ϕ), and Γ . We propose a hybrid iterative algorithm with regularization to compute approximate solutions of the THVI, and we present the convergence analysis of the proposed iterative algorithm. [ABSTRACT FROM AUTHOR]