In this paper, we establish some sufficient conditions for the existence of a solution equilibrium problem. The problem is understood in general form: find $ \overline{x}\in E such that$ \begin{equation*} \Phi(\overline{x},y) \vartriangleleft (-D\backslash\{0\})^c \text{ all }y \in E; \end{equation*} $and its variants, where Boolean-valued bifunction and \Phi multivalued mapping with values vec...

We consider an equilibrium problem defined on a convex set, whose cost bifunction may not be monotone. We show that this problem can be solved by the inexact partial proximal method with quasi distance. As an application, at the psychological level of behavioral dynamics, this paper shows two points: i) how a dual equilibrium problem offers a model of behavioral trap, “easy enough to reach, dif...

We consider stable signal recovery in `q quasi-norm for 0 < q ≤ 1. In this problem, given a measurement vector y = Ax for some unknown signal vector x ∈ R and a known matrix A ∈ Rm×n, we want to recover z ∈ R with ‖x − z‖q = O(‖x − x‖q) from a measurement vector, where x∗ is the s-sparse vector closest to x in `q quasi-norm. Although a small value of q is favorable for measuring the distance to...

In this paper, we introduce the concept of ( ) x c h − -pseudomonotonicity. By considering the existence of solutions for the generalized vector equilibrium problems with a continuous selection theorem, we obtain some existence results for the generalized vector equilibrium problems with point-to-set mappings.

The Muttalib–Borodin biorthogonal ensemble is a joint density function for n particles on the positive real line that depends on a parameter θ. There is an equilibrium problem that describes the large n behavior. We show that for rational values of θ there is an equivalent vector equilibrium problem.

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...

The aim of this work is to analyze lexicographic equilibrium problems on a topological Hausdorff vector space X, and their relationship with some other vector equilibrium problems. Existence results for the tangled lexicographic problem are proved via the study of a related sequential problem. This approach was already followed by the same authors in the case of variational inequalities.