In this work we introduce a system of inclusion problems, which can be regarded as a generalization of the system of equilibrium problems, the system of variational inequality problems, the system of optimization problems, and the inclusion problems. For suitable conditions, we prove an existence result for this system. As applications, we give some existence theorems for the system of equilibr...

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

Variational inequality modeling, analysis and computations are important for many applications, but most of the subject has been developed in a deterministic setting with no uncertainty in a problem’s data. In recent years research has proceeded on a track to incorporate stochasticity in one way or another. However, the main focus has been on a rather limited idea of what a stochastic variation...

In this work, we consider systems of quasi-equilibrium problems with lower and upper bounds and establish the existence of their solutions by using some known maximal element theorems for a family of multivalued maps. Our problems are more general than the one posed in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31]. As a p...

We introduce a new hybrid extragradient viscosity approximationmethod for finding the common element of the set of equilibrium problems, the set of solutions of fixed points of an infinitely many nonexpansive mappings, and the set of solutions of the variational inequality problems for β-inverse-strongly monotone mapping in Hilbert spaces. Then, we prove the strong convergence of the proposed i...

It is known that vector variational inequality models arises from vector optimization and vector traac equilibria. In this paper, existence results of a solution for a generalized pre-vector variational inequality and a generalized pre-quasi-vector variational inequality are established. The main condition used is that the underlying vector-valued function is assumed to be cone-quasi-convex. Th...