It is well known that the general variational inequalities are equivalent to the fixed point problems and the Wiener–Hopf equations. In this paper, we use these alternative equivalent formulations to suggest and analyze some new self-adaptive iterative methods for solving the general variational inequalities. Our results can be viewed as a significant extension of the previously known results f...

This paper is devoted to the study of a new class of nonconvex variational inequalities, named general regularized nonconvex variational inequalities. By using the auxiliary principle technique, a new modified predictor–corrector iterative algorithm for solving general regularized nonconvex variational inequalities is suggested and analyzed. The convergence of the iterative algorithm is establi...

h this paper, we use the auxiliary principle technique to suggest a new &ass of predictor-corrector algorithms for solving generalized variational inequalities. The convergence of the proposed method only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. As special cases, we obtain a number of known and new results for solving va,rious cla...

In this paper, we introduce and study a new unified and general class of variational inequalities. We derive the general error estimates for the finite element solutions of variational inequalities. It has been shown that a class of contact problems with friction terms arising in elastostatics can be studied in the framework of variational inequalities. Several special cases, which can be obtai...

In this paper, we introduce a new class of variational inequalities involving two operators. Using the projection technique, we establish the equivalence between the multivalued general variational inequalities and the fixed point problems. This equivalent formulation is used to suggest and analyze some iterative algorithms for solving the multivalued general variational inequalities. We also d...

In this paper, we use the resolvent operator to suggest and analyze two new numerical methods for solving general mixed quasi variational inequalities coupled with new directions and new step sizes. Under certain conditions, the global convergence of the both methods is proved. Our results can be viewed as significant extensions of the previously known results for general mixed quasi variationa...

This paper is devoted to the solvability of generalized mixed variational inequalities in reflexive Banach spaces. We prove the existence of solutions of the generalized mixed variational inequalities for f quasimonotone set-valued mappings without any assumption on bounded values. Furthermore, we give some conditions that guarantee the existence of solutions of the generalized mixed variationa...

In this paper, we introduce and consider a new class of equilibrium variational inequalities, called the mixed general equilibrium bifunction variational inequalities. We suggest and analyze some proximalmethods for solvingmixed general equilibriumbifunction variational inequalities using the auxiliary principle technique. Convergence of these methods is considered under somemild suitable condi...

In this paper we survey the relationships between scalar and vector variational inequalities (of differential type) and the underlying optimization problem. We show that the variational inequalities of Stampacchia type can be viewed as necessary optimality conditions, while the variational inequalities of Minty type can be considered as sufficient optimality conditions. Concerning this last sta...