In this paper, we first prove a generalization of McClendon’s variational inequality for contractible multimaps. Next, using a new generalized variational inequality, we will prove an existence theorem of Nash equilibrium for the generalized game G = (Xi;Ti, fi)i∈I in a finite dimensional Riemannian manifold. A suitable example for Nash equilibrium is given in a geodesic convex generalized game...

The concept of η-invex set is explored and the concept of T-η-invex function is introduced. These concepts are applied to the generalized vector variational inequality problems in ordered topological vector spaces. The study of variational inequality problems is extended to H-spaces and differentiable n-manifolds. The solution of complementarity problem is also studied in the presence of fixed ...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

The alternating direction method is an attractive method for a class of variational inequality problems if the subproblems can be solved efficiently. However, solving the subproblems exactly is expensive even when the subproblem is strongly monotone or linear. To overcome this disadvantage, this paper develops a new alternating direction method for cocoercive nonlinear variational inequality pr...

In this paper, we design a new projection-type alternating direction method which is an attractive method for solving variational inequality problems, and its application range covers linear programming, semidefinite programming etc. In each iteration, it just solves a linear equation and implements three orthogonal projections to closed convex sets. Under the conditions of monotonicity and Lip...

The purpose of this paper is using Korpelevich’s extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approxima...

In this paper, we suggest and analyze a new iterative method for solving some variational inequality involving an accretive operator in Banach spaces. We prove the strong convergence of the proposed iterative method under certain conditions. As a special of the proposed algorithm, we proved that the algorithm converges strongly to the minimum norm solution of some variational inequality. AMS su...

A class of implicit multivalued vector equilibrium problems is studied. By using the generalized Fan-Browder fixed point theorem, some existence results of solutions for the implicit multivalued vector equilibrium problems are obtained under some suitable assumptions. Moreover, a stability result of solutions for the implicit multivalued vector equilibrium problems is derived. These results ext...

This paper presents novel results about the structure of solutions for certain evolutionary variational inequality problems. We show that existence of piecewise solutions is dependant upon the form of the constraint set underlying the evolutionary variational inequality problem considered. We discuss our results in the context of double-layered dynamics theory and we apply them to the modelling...

A competitive economic equilibrium problem involving utility functions is considered. The equilibrium problem is reformulated by means of a quasi-variational inequality and an existence result of equilibrium under weaker assumption than strong monotonicity is obtained. In this more general setting, when the excess demand operator is not a single valued-map, we are led to study a generalized var...