Implicit Iterative Method for Hierarchical Variational Inequalities

Implicit and explicit iterative algorithms for hierarchical variational inequality in uniformly smooth Banach spaces

The purpose of this paper is to solve the hierarchical variational inequality with the constraint of a general system of variational inequalities in a uniformly convex and 2-uniformly smooth Banach space. We introduce implicit and explicit iterative algorithms which converge strongly to a unique solution of the hierarchical variational inequality problem. Our results improve and extend the corr...

The Solvability of a Class of General Nonlinear Implicit Variational Inequalities Based on Perturbed Three-Step Iterative Processes with Errors

We introduce and study a new class of general nonlinear implicit variational inequalities, which includes several classes of variational inequalities and variational inclusions as special cases. By applying the resolvent operator technique and fixed point theorem, we suggest a new perturbed three-step iterative algorithm with errors for solving the class of variational inequalities. Several exi...

Projection Iterative Approximations for a New Class of General Random Implicit Quasi-variational Inequalities

We introduce a class of projection-contraction methods for solving a class of general random implicit quasi-variational inequalities with random multivalued mappings in Hilbert spaces, construct some random iterative algorithms, and give some existence theorems of random solutions for this class of general random implicit quasi-variational inequalities. We also discuss the convergence and stabi...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems