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...

This paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  We use variational methods to investigateseveral aspects of propagating waves, including localization (seeFigure 1), existence criteria and the formulas to find them. Weapproach the problem using two complementary methods: Thevariational methods fo...

We use the auxiliary principle technique to suggest and analyze some iterative methods for solving a new class of variational inequalities, which is called the mixed trifunction variational inequality. The mixed trifunction variational inequality includes the trifunction variational inequalities and the classical variational inequalities as special cases. Convergence of these iterative methods ...

Correspondence: chwhappy@163. com Department of Science, Nanchang Institute of Technology, Nanchang 330099, P. R. China Abstract In this article, we introduce and study a new system of generalized quasi-variationallike inclusions with noncompact valued mappings. By using the h-proximal mapping technique, we prove the existence of solutions and the convergence of some new N-step iterative algori...

The main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by the means of the proximal subdifferential of the no...

We discuss equilibria, dynamics and regularity for Smoluchowski equations coupled to Navier-Stokes equations. Introduction We consider mixtures of fluids and microscopic inclusions. The microscopic inclusions are characterized by state variables m ∈ M , where M is a compact smooth Riemannian manifold without boundary. The simplest example is that of microscopic rods with directors m ∈ S. The mi...

We introduce and study a class of generalized strongly nonlinear mixed variational-like inequalities, which includes several classes of variational inequalities and variational-like inequalities as special cases. By applying the auxiliary principle technique and KKM theory, we suggest an iterative algorithm for solving the generalized strongly nonlinear mixed variationallike inequality. The exi...

the aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. the state and co-state are approximated by the lowest order raviart-thomas mixed finite element spaces and the control is not discreted. optimal error estimates in l2 are established for the state...