Abstract

This paper deals with the set-valued vector quasiequilibrium problem of finding a point (z0,x0) 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,η),C(z0,x0,η)) ∈ α, where α is a subset of 2Y × 2Y and A : E × K → 2K,B : E × K → 2E,F : E ×K ×K → 2Y , C : E ×K ×K → 2Y are set-valued maps, with Y is a topological vector space. Two existence theorems are proven under different assumptions. Correct results of [Hou, S.H., Yu, H., Chen, G.Y.: J. Optim. Theory Appl. 119, 485–498 (2003)] are obtained from a special case of one of these theorems.