Gauss-Seidel Type Algorithms for a Class of Variational Inequalities

Abstract

In this paper, we consider a new system of extended general quasi
variational inequalities involving six nonlinear operators. Using projection op-
erator technique, we show that system of extended general quasi variational
inequalities is equivalent to a system of xed point problems. Using this al-
ternative equivalent formulation, we propose and analyze Gauss-Seidel type
algorithms for solving a system of extended general quasi variational inequali-
ties. Convergence of new method is discussed under some suitable conditions.
Several special cases are discussed. Results obtained in this paper continue to
hold for these problems.