We apply an existence theorem of variational inclusion problem on metric spaces to study optimization problems, set-valued vector saddle point problems, bilevel problems, and mathematical programs with equilibrium constraint on metric spaces. We study these problems without any convexity and compactness assumptions. Our results are different from any existence results of these types of problems...

Nikishin systems of three functions are considered. For such systems, the rate of convergence of simultaneous interpolating rational approximations with partially prescribed poles is studied. The solution is described in terms of the solution of a vector equilibrium problem in the presence of a vector external field.

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...

This paper concerns equilibrium problems in real metric linear spaces. Considering a modified notion of  upper sign property for bifunctions, we obtain the relationship between the solution sets of the local Minty equilibrium problem and the equilibrium problem, where the technical conditions on $f$ used in the literature are relaxed. The KKM technique is used to generalize and unify some exist...

We consider the two matrix model with an even quartic potential W (y) = y/4+αy/2 and an even polynomial potential V (x). The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices M1. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and ...

a central problem ill empirical macroeconomics is to determine when and how much the exchange rate is misaligned. this paper clarifies and calculates the concept of’ the equilibrium real exchange rate, using a structural vector auto regression (var) model. by imposing long—run restrictions on a var model for iran, lour structural shocks are identified: nominal demand, real demand, supply and oi...

The traffic assignment problem aims to calculate an equilibrium route flow vector, generally by seeking a zero of an appropriate objective function. If a continuous dynamical system follows a descent direction for this objective function at each non-equilibrium route flow vector, the system converges to equilibrium. It is shown that when this dynamical system is discretised with a fixed step le...

Vector field approximation is a problem involving the reconstruction of physical fields from a set of scattered observed data. In this paper, we address the problem of interpolation of divergence-free vector fields in three dimensional space by thin plate spline under tension. The problem is formulated as a minimization problem where the cost is related to the equilibrium energy of thin plate w...

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...

In this paper, we establish the existence theorems of simultaneous equilibriums. As consequence of our results, we establish the existence theorem of simultaneous mathematical program and equilibrium problem and existence theorems of generalized vector quasi-saddle point problems .