Selection Theorem,Coincidence Theorem And Vector Quasi-quilibrium Problem In Generalized Convex Spaces

In this paper,a new type of generalized vector quasi-equilibrium problem is introduced.in order to obtain its existence theorems in G -convex spaces,a coincidence theorem,a continuous selection theorem and a fixed point theorem in G -convex spaces are first established.These theorems themselves are interesting. Then using these results and the scalarization method,we prove existence theorems for the new type of generalized vector quasi-equilibrium problem and a minimax theorem in G -convex spaces.As applications,the solutions of vector variational inequlities and a vector optimization problem are derived.