Generalized bi-quasi-variational-like inequalities on non-compact sets
Commun. Korean Math. Soc. 2017 Vol. 32, No. 4, 933-957
Published online October 31, 2017
Yeol Je Cho, Mohammad S. R. Chowdhury, Je Ai Ha
Gyeongsang National University, University of Management and Technology (UMT), Gyeongsang National University
Abstract : In this paper, we prove some existence results of solutions for a new class of generalized bi-quasi-variational-like inequalities (GBQVLI) for ($\eta$-$h$)-quasi-pseudo-monotone type I and strongly ($\eta$-$h$)-quasi-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. To obtain our results on GBQVLI for ($\eta$-$h$)-quasi-pseudo-monotone type I and strongly ($\eta$-$h$)-quasi-pseudo-monotone type I operators, we use Chowdhury and Tan's generalized version of Ky Fan's minimax inequality as the main tool.
Keywords : generalized bi-quasi-variational-like inequalities, ($\eta$-$h$)-quasi-pseudomonotone type I operators, locally convex Hausdorff topological vector spaces
MSC numbers : 49J30, 47H10, 47H17, 49M05
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