- AN EXTENSION OF MULTI-VALUED QUASI-GENERALIZED SYSTEM
- Kum, Sangho ; Kim, Won Kyu ;
- Journal of the Chungcheong Mathematical Society , volume 25, issue 4, 2012, Pages 703~709
- DOI : 10.14403/jcms.2012.25.4.703

Abstract

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. Next, in [10], the first author considered a generalization of (GS) into a multi-valued circumstance called the multi-valued quasi-generalized system (in short, MQGS). In the current work, we provide an extension of (MQGS) into a system of (MQGS) in general settings. This system is called the generalized multi-valued quasi-generalized system (in short, GMQGS). Using the existence theorem for abstract economy by Kim [8], we prove the existence of solutions for (GMQGS) in the framework of Hausdorff topological vector spaces. As an application, an existence result of a system of generalized vector quasi-variational inequalities is derived.