in this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in hilbert spaces.

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...

The approximate solvability of a generalized system for strongly accretive nonlinear variational inequalities in q−uniformly smooth Banach spaces is studied, based on the convergence of sunny nonexpansive retraction projection methods. The results presented in this paper extend and improve the main results of R.U.Verma[General convergence analysis for two-step projection methods and application...

The variational inequality problem provides a broad unifying setting for the study of optimization, equilibrium and related problems and serves as a useful computational framework for the solution of a host of problems in very diverse applications. Variational inequalities have been a classical subject in mathematical physics, particularly in the calculus of variations associated with the minim...

Contact phenomena abound, and play an important role in structural and mechanical engineering. Owing to their inherent complexity, they are modelled by highly nonlinear inequalities. Considerable progress has been achieved in modelling, variational analysis and numerical approximations of contact problems involving viscoelastic and viscoplastic materials. Moreover, it has led to several new typ...

It is well known that gap functions play a major role in developing error bounds for strongly monotone and affine monotone variational inequalities. However the error bound would be important from the point of view of computation if the gap function values diminishes on sequence of points which converge to a solution of the variational inequality. A gap function exhibiting such behavior is term...

Variational inequalities over sets deened by systems of equalities and inequalities are considered. A continuously diierentiable merit function is proposed whose unconstrained minima coincide with the KKT-points of the variational inequality. A detailed study of its properties is carried out showing that under mild assumptions this reformulation possesses many desirable features. A simple algor...

In this paper, we use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our method includes the two-step forward-backward splitting and extragradient methods for solving various cl...

In this article, we introduce and consider the three-step iterative algorithms for solving a new system of generalized mixed variational inequalities involving different three multi-valued operators. In this study, we use a generalized f-projection method for finding the solutions of generalized system of mixed variational inequalities in Banach spaces. Our result in this article improves and g...

Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set methods that solve only one linear system of equations per iteration. The linear solver, preconditioner, and matrix structures can be chosen by the user for a pa...