• East Asian mathematical journal
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• v.26 no.3
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• pp.415-421
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• 2010

Many kinds of Minty's lemmas show that Minty-type variational inequality problems are very closely related to Stampacchia-type variational inequality problems. Particularly, Minty-type vector variational inequality problems are deeply connected with vector optimization problems. Liu et al. [10] considered vector variational inequalities for setvalued mappings by using scalarization approaches considered by Konnov [8]. Lee et al. [9] considered two kinds of Stampacchia-type vector variational inequalities by using four kinds of Stampacchia-type scalar variational inequalities and obtain the relations of the solution sets between the six variational inequalities, which are more generalized results than those considered in [10]. In this paper, the author considers the Minty-type case corresponding to the Stampacchia-type case considered in [9].

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.401-410
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• 2007

Some existence theorems of solutions of a new class of generalized vector F-implicit complementarity problems with the corresponding generalized vector F-implicit variational inequality problems were established.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.279-287
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• 2004

In this paper, we establish relations between a solution of a vector continuous-time program and a solution of a vector variational-type inequality problem with functionals.

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.299-306
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• 2018

In this paper, we prove the existence results of the solutions for vector variational inequality problems by using the ${\parallel}{\cdot}{\parallel}$-sequentially continuous mapping.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.455-464
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• 2007

We consider existence theorems for a new class of mixed vector F-implicit complementarity problems and the corresponding mixed vector F-implicit variational inequality problems.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.319-324
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• 2009

In a series of papers [3, 4, 5], the author developed the generalized vector variational inequality with operator solutions (in short, GOVVI) by exploiting variational inequalities with operator solutions (in short, OVVI) due to Domokos and $Kolumb\acute{a}n$ [2]. In this note, we give an extension of the previous work [4] in the setting of Hausdorff locally convex spaces. To be more specific, we present an existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [7] within the framework of (GOVVI).

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.423-432
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• 2008

In this paper, we consider a new Minty's Lemma for strong implicit vector variational inequality systems and obtain some existence results for systems of strong implicit vector variational inequalities which generalize some results in [1].

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.289-295
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• 2020

Minkowski's inequality is one of the most famous inequalities in mathematics, and has many applications. In this paper, we give Minkowski's inequality for generalized variational integrals that are based on a supermultiplicative function. Our results include previous results about fractional integral inequalities of Minkowski's type.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.45-55
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• 1996

Recently, Giannessi [1] introduced a vector variational inequalityy for vector-valued functions in an Euclidean space. Since then, Chen et al. [2-6], Lee et al. [7], and Yang [8] have intensively studied vector variational inequalities for vector-valued functions in abstract spaces.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.665-673
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• 2006

In a recent paper, Domokos and $Kolumb\'{a}}n$ [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multivalued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4].