• East Asian mathematical journal
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• v.26 no.1
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• pp.49-58
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• 2010

In this paper, we consider and study a new class of generalized vector quasi-variational type inequalities and obtain some existence theorems for both under compact and noncompact assumptions in topological vector spaces without using monotonicity. For the noncompact case, we use the concept of escaping sequences.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.933-957
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• 2017

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.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.825-839
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• 2024

A new type of more general form of variational inequalities for quasi-pseudo-monotone type III and strong quasi-pseudo-monotone type III operators has been obtained on compact domains in locally convex Hausdorff topological vector spaces. These more general forms of variational inequalities for the above types of operators used the more general form of minimax inequality by Chowdhury and Tan in [3] as the main tool to derive them. Our new results established in this paper should have potential applications in nonlinear analysis and related applications, e.g., see Aubin [1], Yuan [11] and references wherein.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.743-756
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• 2022

We obtained results on upper hemi-continuous and pseudo-monotone type two mappings for sets which are not compact. M.S.R. Chowdhury and K.-K. Tan's improved result on Ky Fan's minimax inequality will be used.