Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type I operators on non-compact sets

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type I operators in non-compact settings in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type I operators in non-compact settings, we shall use the concept of escaping sequences introduced by Border [2] by applying Chowdhury and Tan’s result on generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type I operators on compact sets [11]. As an application, an existence theorem on generalized bi-complementarity problem for quasi-pseudo-monotone type I operators is given in non-compact settings. AMS Subject Classification: 47H05