• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권3호
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• pp.281-288
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• 2012

In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.47-55
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• 2002

In this pope., we consider a Minty's lemma for ($\theta ,\eta$)-pseudomonotone-type set-valued mappings in real Banach spaces and then we show the existence of solutions to variational-type inequality problems for ($\theta ,\eta$)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.819-827
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• 2009

In this paper, we introduce new pseudomonotonicity and proper quasimonotonicity with respect to a given function, and show some existence results for strong implicit vector variational inequalities by considering new generalized Minty's lemma. Our results generalize and extend some results in [1].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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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].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권1호
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• pp.33-37
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• 1999

We obtain a generalization of Behera and Panda's result on nonlinear scalar case to the vector version.

• 대한수학회논문집
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• 제14권2호
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• pp.319-328
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• 1999

In this paper we consider a kind of Minty`s lemma for multifunctions in Banach spaces, and apply it to obtain existence theorems for two kinds of variational-like inequalities using the KKM-Fan theorem.