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Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets
(Maltepe Üniversitesi, 2009) Chowdhury, Mohammad Showkat Rahim
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 II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudomonotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version in [M. S. R. Chowdhury and K.-K. Tan, Generalization of Ky Fan’s minimax inequality with applications to generalized variational inequalities for pseudo-monotone operators and fixed point theorems, J. Math. Anal. Appl. 204 (1996), 910–929] of Ky Fan’s minimax inequality in [K. Fan, A minimax inequality and applications, in “Inequalities, III” (O. Shisha, Ed.), pp.103-113, Academic Press, San Diego, 1972] as the main tool.