Variational inequalities represent very useful and powerful tools for investigation and solution of many equilibrium type problems arising in Economics, Engineering, Operations Research and Mathematical Physics. The talk is devoted to several rather new approaches from [1]–[5] to construction of solution methods for variational inequalities with multi-valued cost mappings. We recall that the pr...

Because of their applications in economics, game theory, mathematical physics, operations research and other areas, many classes of vector variational inequalities were intensively studied. For existence of solutions, resolution methods or equivalence with equilibrium and optimization problems see, for example, [11], [14], [15], [19], [17] and the references therein. For the study of variationa...

We consider variational inequality problems for set-valued vector fields on general Riemannian manifolds. The existence results of the solution, convexity of the solution set, and the convergence property of the proximal point algorithm for the variational inequality problems for set-valued mappings on Riemannian manifolds are established. Applications to convex optimization problems on Riemann...

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...

The problems which imply variational inequality over product sets have many applications. Thus, the Nash equilibrium problem for differentiable functions, various equilibrium-type problems, as traffic equilibrium, spatial equilibrium and general equilibrium programming problems from economics, game theory, operations research, mathematical physics, for example, can be modelled as variational in...

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

We introduce new and interesting model of system of generalized set-valued equilibrium problems which generalizes and unifies the system of set-valued equilibrium problems, the system of generalized implicit vector variational inequalities, the system of generalized vector and vector-like variational inequalities introduced by Ansari et al. (2002), the system of generalized vector variational i...

In this paper, we consider the algorithm proposed in recent years by Censor, Gibali and Reich, which solves split variational inequality problem, and Korpelevich's extragradient method, which solves variational inequality problems. As our main result, we propose an iterative method for finding an element to solve a class of split variational inequality problems under weaker conditions and get a...