# zbMATH — the first resource for mathematics

The system of vector quasi-equilibrium problems with applications. (English) Zbl 1073.90032
Summary: We consider the system of vector quasi-equilibrium problems with or without involving $$\Phi$$-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 equilibrium problem for vector-valued functions. As an application, we derive some existence results for a solution to the Debreu type equilibrium problem for vector-valued functions.

##### MSC:
 90C27 Combinatorial optimization 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 91A40 Other game-theoretic models 49J40 Variational inequalities 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics 91B50 General equilibrium theory
Full Text: