A REMARK ON MULTI-VALUED GENERALIZED SYSTEM

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single- valued bi-operator F. In this note, we aim at an extension of(GS) due to Kazmi and Khan [7] into a multi-valued circumstance. We consider a fairly general problem called the multi-valued quasi- generalized system (in short, MQGS). Based on the existence of 1-person game by Ding, Kim and Tan [5], we give a generalization of (GS) in the name of (MQGS) within the framework of Hausdor？？ topological vector spaces. As an application, we derive an existence result of the generalized vector quasi-variational inequality problem. This result leads to a multi-valued vector quasi-variational inequal-ity extension of the strong vector variational inequality (SVVI) due to Fang and Huang [6] in a general Hausdor？？ topological vector space.