It is well known that variational inequalities are systematically used in the theory of many practical problems related to ”equilibrium”. The equilibrium is an important state considered in Physics, Engineering, Sciences and Economics and even in Biology, [5], [37], [38], [24], [56]. When a variational inequality is defined on a closed convex set, which is in particular a closed convex cone, in...

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...

Traffic network equilibrium problems with capacity constraints of arcs are studied. A weak vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin 2010 , and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a weak vector equilibrium flow to be a parametric equilibrium flow are de...

In this paper, we consider the system of vector quasi-equilibrium problems with or without involving -condensing maps and prove the existence of its solution. Consequently, we get existence results for a solution to the system of vector quasi-variational-like inequalities. We also prove the equivalence between the system of vector quasi-variational-like inequalities and the Debreu type equilibr...

The purpose of this paper is to study a split hierarchical monotone variational inclusion problem which includes split variational inequality problems, split common fixed point problems, split monotone variational inclusion problems, split convex minimization problems, etc., as special cases, and fixed point problems for nonexpansive semigroup in the setting of Hilbert spaces. For solving this ...

Background Equilibrium is a central concept in numerous disciplines including economics, management science/operations research, and engineering. Methodologies that have been applied to the formulation , qualitative analysis, and computation of equilibria have included • systems of equations, • optimization theory, • complementarity theory, and • fixed point theory. Variational inequality theor...

The regularity of a solution to the variational inequality for the Stokes equation is considered. The inequality describes the steady motion of the viscous incompressible uid under a certain unilateral constrain of friction type. Firstly the solution is approximated by solutions to a regularized problem which is introduced by Yosida's regularization for a multi-valued opearator. Then we establi...

In this paper, we consider mixed vector variational-like inequality problems in the setting of topological vector spaces. We extend the concept of upper sign continuity for vector-valued mappings. Further, by exploiting KKM-Fan lemma, we establish some existence results for solutions of mixed vector variational-like inequality problems and show that the solution sets of these problems are compact.

In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon's bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the...