A generalized quasi-equilibrium problem

In this paper, using the Kakutani-Fan-Glicksberg fixed point theorem, we obtain an existence theorem for a generalized vector quasi-equilibrium problem of the following type: for a suitable choice of the sets X, Z and V and of the mappings T : X (sic) X, R : X (sic) X, Q : X (sic) Z, F : X x X x Z (sic) V, C : X --- V, find ((x) over tilde) is an element of X such that (x) over tilde is an element of T((x) over tilde) and (for all)y is an element of R((x) over tilde), (alpha)z is an element of Q((x) over tilde), p(F(((x) over tilde ,y,z), C((x) over tilde)), where rho is a given binary relation on 2(V) and alpha is any of the quantifiers for all, there exists. Finally, several particular cases are discussed and some applications are given.