In this paper, we propose two new methods for solving mixed quasi variational inequalities by using the resolvent operator technique. Under certain conditions, the global convergence of the both methods is proved. The skew-symmetry of the nonlinear bifunction plays a crucial part in the convergence analysis of these new iterative methods. The comparison of these methods with other methods for s...

A spectral-element technique to approximate partial diierential equations on an innnite domain is examined. The method is based on Boyd's mapping of a semi-innnite interval to a nite interval, and it is extended to a variational setting which allows for an implementation using a spectral-element method. By extending the method to a variational form, a straightforward implementation allows for h...

In this paper, we suggest and analyze some iterative methods for solving the system of nonconvex variational inequalities with two nonlinear mappings by using the projection technique. We show that the strong convergence of these iterative methods to the solutions of the system of nonconvex variational inequalities. Consequently, the results presented in this paper can be viewed as an improveme...

We study a new system of nonlinear set-valued variational inclusions involving a finite family of H ·, · -accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family of H ·, · -accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variational inclusions. Moreover, we introduce a new iterative scheme...

We consider the optimization problem of dividends and risk exposures of a firm in the diffusion model with linear costs. The variational inequality associated with this problem is given by the nonlinear form of elliptic type. Using the viscosity solutions technique, we solve the corresponding penalty equation and show the existence of a classical solution to the variational inequality. The opti...