Abstract

In this paper we consider the generalized vector equilibrium problem (P α ) of finding a point (z 0 ,x 0 )∈E×K such that x 0 ∈A(z 0 ,x 0 ) and ∀η∈A(z 0 ,x 0 ),∃z∈B(z 0 ,x 0 ,η),(F(z,x 0 ,η),C(z,x 0 ,η))∈α, where α is an arbitrary relation on 2 Y, and A, B, C and F are set-valued maps between finite-dimensional spaces. Existence results are obtained under assumptions different from those of P. H. Sach [”On a class of generalized vector equilibrium problems with set-valued maps”, Preprint 05-07, Hanoi Inst. Math., Hanoi, 2005; per bibl.]. Some special cases of Problem (P α ) are discussed in detail.