An existence theorem for generalized quasi-variational inequalities (Q2366674)

The generalized quasi-variational inequality problem ``Find \(\widehat x\), \(\widehat z\) such that (P): \(\widehat x\in \Gamma(\widehat x)\), \(\widehat z\in \Phi(\widehat x)\), \(\langle\widehat z,\widehat x-y\rangle\leq 0\) \(\forall y\in \Gamma(\widehat x)\)'', where \(\Phi\) and \(\Gamma\) are multifunctions from a subset of \(\mathbb{R}^ n\) into \(\mathbb{R}^ n\), was introduced by \textit{D. Chan} and \textit{J. S. Pang} [Mat. Oper. Res. 7, 211- 222 (1982; Zbl 0502.90080)]. The author obtains an existence theorem for (P) under substantially weaker conditions than that obtained by D. Chan and J. S. Pang.