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In this paper, we study vector quasiequilibrium problems. After that, the Painlev´e-Kuratowski upper convergence, lower convergence and convergence of the approximate solution sets for these problems are investigated by using a sequence of mappings ΓC -converging. As applications, we also consider the Painlev´e-Kuratowski upper convergence of the approximate solution sets in the special cases of variational inequality problems of the Minty type and Stampacchia type. The results presented in this paper extend and improve some main results in the literature.

Painleve-Kuratowski convergences of the approximate solution sets for vector quasiequilibrium problems