Existence results for strong vector equilibrium problems and their applications

Abstract

New existence results for the strong vector equilibrium problem are presented,relying on a well-known separation theorem in infinite-dimensional spaces. The main results are applied to strong cone saddle-points and strong vector variational inequalities providing new existence results, and furthermore they allow recovery of an earlier result from the literature

Existence of equilibrium for generalized games in choice form and applications

“…The importance of vector equilibrium problems comes, obviously, from the great number of recent papers dedicated to the study of the existence of their solutions. We can provide a short list of references presented in our bibliography: [1][2][3][4][5], [7], [9], [10], [14][15][16][17][18], [21][22][23][24][25], [29]. From the scientific point of view, we must state the fact that the vector equilibrium problems unifies several problems, among which we can mention: vector variational inequalities, vector complementarity problems and vector optimizations problems.…”

Existence Theorems ofε-Cone Saddle Points for Vector-Valued Mappings

“…In recent years, based on the development of vector optimization, a great deal of papers have been devoted to the study of cone saddle points problems for vectorvalued mappings and set-valued mappings, such as [1][2][3][4][5][6][7][8]. Nieuwenhuis [5] introduced the notion of cone saddle points for vector-valued functions in finite-dimensional spaces and obtained a cone saddle point theorem for general vectorvalued mappings.…”

“…Li et al [4] obtained an existence theorem of lexicographic saddle point for vector-valued mappings. Bigi et al [1] obtained a cone saddle point theorem by using an existence theorem of a vector equilibrium problem. Zhang et al [9] established a general cone loose saddle point for set-valued mappings.…”

Optimality conditions for vector equilibrium problems and their applications

“…A large number of results for different vector equilibrium problems are established, such as existence of solutions (see, for instance, [2,3,4,5,6,7,8,10,16,21]), well-posedness (see, for instance, [1,9,31]), sensitivity analysis (see, for instance, [24,25]). But, as far as we know, there are only a few papers concerned with optimality conditions for solutions.…”

“…Later on, this inequality was called equilibrium problem by Blum and Oettli [11]. The vector equilibrium problems include vector optimization problems, vector variational inequality problems, vector complementarity problems, and cone saddle point problems, as particular cases.A large number of results for different vector equilibrium problems are established, such as existence of solutions (see, for instance, [2,3,4,5,6,7,8,10,16,21]), well-posedness (see, for instance, [1, 9, 31]), sensitivity analysis (see, for instance, [24,25]). But, as far as we know, there are only a few papers concerned with optimality conditions for solutions.…”