Sentence examples for a solution of equilibrium from inspiring English sources

Numerous problems in physics, optimization, and economics reduce to find a solution of equilibrium problem.

Thus EP ( g ) : = { z ∈ C : g ( z, y ) ≥ 0, ∀ y ∈ C }. Numerous problems in physics, optimization and economics reduce to finding a solution of equilibrium problem.

The equilibrium problem is to find x ∗ ∈ C such that F ( x ∗, y ) ≥ 0, for all y ∈ C. We shall denote the solutions set of the equilibrium problem by E P ( F ). Numerous problems in physics, optimization, and economics reduce to find a solution of equilibrium problem.

The purpose of this paper is to introduce a split equilibrium problem (SEP) and find a solution of the equilibrium problem such that its image under a given bounded linear operator is a solution of another equilibrium problem.

From (1.1) and (1.2), we can see that the SEP contains two equilibrium problems, and the image of a solution of one equilibrium problem under a given bounded linear operator is a solution of another equilibrium problem.

Since many problems coming from physics, optimization, and economics reduce to find a solution of the equilibrium problem (1.1) (see, for instance, [1, 2]), the equilibrium problem (1.1) is very important in the field of applied mathematics.

Finally, we consider finding a solution of the equilibrium problem.

The following lemma gives a characterization of a solution of an equilibrium problem.

In this section, we consider the problem of approximating a solution of the equilibrium problem.

Numerous problems in physics, optimization and economics reduce to finding a solution of the equilibrium problem.

where u ∈ K is a solution of the equilibrium problem (2.5).