Abstract
We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.
Highlights
Introduction and FormulationsThroughout the paper, we will adopt the following terminology and notations
We introduce and consider the following triple hierarchical variational inequality problem (THVIP)
Let V : C → H be a ρ-contraction with coefficient ρ ∈ [0, 1), S : C → C be a nonexpansive mapping, and, for i = 1, 2, Ti : C → C be ζi-strictly pseudocontractive mapping with Fix(T1) ∩ Fix(T2) ≠ 0
Summary
Introduction and FormulationsThroughout the paper, we will adopt the following terminology and notations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
