- A REMARK ON MULTI-VALUED GENERALIZED SYSTEM
- Kum, Sang-Ho ;
- Journal of the Chungcheong Mathematical Society , volume 24, issue 2, 2011, Pages 163~169
Abstract
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 Hausdorff 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 Hausdorff topological vector space.