Abstract

Existence theorems are given for the problem of finding a point (z 0,x 0) of a set E × K such that (z0,x0)∈B(z0,x0)×A(z0,x0) and, for all η∈A(z0,x0),(F(z0,x0,x0,η),C(z0,x0,x0,η))∈α where α is a relation on 2Y (i.e., a subset of 2Y × 2Y), A:E×K⟶2K, B:E×K⟶2E,C:E×K×K×K⟶2Y and F:E×K×K×K⟶2Y are some set-valued maps, and Y is a topological vector space. Detailed discussions are devoted to special cases of α and C which correspond to several generalized vector quasi-equilibrium problems with set-valued maps. In such special cases, existence theorems are obtained with or without pseudomonotonicity assumptions.