The purpose of this paper is to study the existence and convergence analysis of the solutions of the system of mixed variational inequalities in Banach spaces by using the generalized f projection operator. The results presented in this paper improve and extend important recent results of Zhang et al. 2011 and Wu and Huang 2007 and some recent results.

The remarkable theorem of P. Belinskii is a deep underlying result in the variational calculus for quasiconformal maps. It valid only maps with small sufficiently regular Beltrami coefficients. We provide global version this connected classical results on extensions conformal and its new applications.

This paper is concerned with variational methods applied to functionals of the calculus variations in a multi-dimensional case. We prove existence multiple critical points for symmetric functional whose principal part not subjected any upper growth condition. For this purpose, nonsmooth are applied.

This paper introduces new types of Euler-Lagrange PDEs required by optimal control problems with performance criteria involving curvilinear or multiple integrals subject to evolutions of multidimensional-flow type. Particularly, the anti-trace multi-time Euler-Lagrange PDEs are strongly connected to the multi-time maximum principle. Section 1 comments the limitations of classical multi-variable...

In this paper, we establish a new version of Ekeland’s variational principle in a new setting of cone pseudo-quasimetric spaces. In constrast to metric spaces, we do not require that each forward Cauchy sequence is forward convergent and that each forward convergent sequence has the unique forward limit. The motivation of this paper comes from applications in Behavioral Sciences since a cone ps...

Variational inequalities and even quasi-variational inequalities, as means of expressing constrained equilibrium, have utilized geometric properties of convex sets, but the theory of tangent cones and normal cones has yet to be fully exploited. Much progress has been made in that theory in recent years in understanding the variational geometry of nonconvex as well as convex sets and applying it...

There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes framework in the context of finite element exterior calculus. However, we are not aware of any numerical experiments where mixed finite elements derived from discretizations of exterior calculus are used for a surface do...

Concepts of conditioning have long been important in numerical work on solving systems of equations, but in recent years attempts have been made to extend them to feasibility conditions, optimality conditions, complementarity conditions and variational inequalities, all of which can be posed as solving “generalized equations” for set-valued mappings. Here, the conditioning of such generalized e...

This paper proposes a new extragradient solution method for strongly pseudomonotone variational inequalities. A detailed analysis of the convergence of the iterative sequences and the range of application of the method is given. Mathematics Subject Classification (2010). 47J20, 49J40, 49M30.