×

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
PDF BibTeX XML Cite
Full Text: DOI