• Journal of the Korean Mathematical Society
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• v.30 no.2
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• pp.433-446
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• 1993

• 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.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.781-792
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• 2021

In this paper, we study well-posed problems and variational inequalities in locally convex Hausdorff topological vector spaces. The necessary and sufficient conditions are obtained for the existence of solutions of variational inequality problems and quasi variational inequalities even when the underlying set K is not convex. In certain cases, solutions obtained are not unique. Moreover, counter examples are also presented for the authenticity of the main results.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.371-377
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• 1999

The purpose of this paper is to provide two examples which prove that Cubiotti's theorem and Yao's one on the generalized quasi-variational inequality problem are independent of each other. In addition, we give another example which tells us that certain conditions are essential in Cubiotti's theorem and Yao's one.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.183-191
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• 2007

In this paper, we introduce and study a new class of equilibrium problems, known as regularized mixed quasi equilibrium problems. We use the auxiliary principle technique to suggest and analyze some iterative schemes for regularized equilibrium problems. We prove that the convergence of these iterative methods requires either pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving equilibrium problems and variational inequalities involving the convex sets.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.273-285
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• 2006

In this paper, we shall give an affirmative answer to the question raised by Kim and Tan [1] dealing with generalized vector quasi-variational inequalities which generalize many existence results on (VVI) and (GVQVI) in the literature. Using the maximal element theorem, we derive two theorems on the existence of weak solutions of (GVQVI), one theorem on the existence of strong solution of (GVQVI), and one theorem on strong solution in the 1-dimensional case.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.05a
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• pp.33-36
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• 2006

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.271-276
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• 2014

Recently, Taji [7] and Harms et al. [4] studied the regularized gap function of QVI analogous to that of VI by Fukushima [2]. Discussions are made in a finite dimensional Euclidean space. In this note, an infinite dimensional generalization is considered in the framework of a reflexive Banach space. To do so, we introduce an extended quasi-variational inequality problem (in short, EQVI) and a generalized regularized gap function of EQVI. Then we investigate some basic properties of it. Our results may be regarded as an infinite dimensional extension of corresponding results due to Taji [7].

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.709-721
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• 2005