Application Of The Auxiliary Principle Technique In Solving A Few Classes Of Variational Inequalities

This paper includes three sections. In the first section, we use the auxiliary principle technique to prove the existence of a solution of a class of set-valued nonlinear mixed variational inequalities and suggest an algorithm generating some iterative sequences which are convergent, then we consider the convergence and stability of another algorithm suggested by the auxiliary principle technique. In the second section, the existence of a solution for a class of variational inequalities for fuzzy mappings and the convergence of iterative sequence are considered, we also discuss the stability of algorithm for solving the class of variational inequalities for classical mappings. In the last section, we introduce and study a class of variational-like inequalities by applying the auxiliary principle technique.