• 대한수학회지
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• 제33권3호
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• pp.609-624
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• 1996

Recently, Giannessi [9] firstly introduced the vector-valued variational inequalities in a real Euclidean space. Later Chen et al. [5] intensively discussed vector-valued variational inequalities and vector-valued quasi variationl inequalities in Banach spaces. They [4-8] proved some existence theorems for the solutions of vector-valued variational inequalities and vector-valued quasi-variational inequalities. Lee et al. [14] established the existence theorem for the solutions of vector-valued variational inequalities for multifunctions in reflexive Banach spaces.

• 대한수학회지
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• 제58권4호
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• pp.1035-1058
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• 2021

Under certain rather weak size conditions assumed on the kernels, some weighted norm inequalities for singular integral operators, related maximal operators, maximal truncated singular integral operators and Marcinkiewicz integral operators in nonisotropic setting will be shown. These weighted norm inequalities will enable us to obtain some vector valued inequalities for the above operators.

• 대한수학회지
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• 제37권4호
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• pp.565-577
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• 2000

We consider regularity questions arising in the degenerate elliptic vector valued variational inequalities -div(｜▽u｜p-2∇u)$\geq$b(x, u, ∇u) with p$\in$(1, $\infty$). It is a generalization of the scalar valued inequalities, i.e., the obstacle problem. We obtain the C1,$\alpha$loc regularity for the solution u under a controllable growth condition of b(x, u, ∇u).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권4호
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• pp.225-232
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• 2003

In this paper, we consider the existence of the solutions to the generalized vector variational-type inequalities for set-valued mappings on Hausdorff topological vector spaces using Fan's geometrical lemma.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1419-1432
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• 2023

In this study, we take into account interval-valued vector optimization problems (IVOP) and obtain their relationships to interval vector variational inequalities (IVVI) of Stampacchia and Minty kind in aspects of convexificators, as well as the (IVOP) LU-efficient solution under the LU-convexity assumption. Additionally, we examine the weak version of the (IVVI) of the Stampacchia and Minty kind and determine the relationships between them and the weakly LU-efficient solution of the (IVOP). The results of this study improve and generalizes certain earlier results from the literature.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권1호
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• pp.70-76
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• 2006

Some Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings was introduced and the existence of solutions to them under non-compact assumption was considered using the particular form of the generalized Ky Fan's section theorem due to Park [15]. As a corollary, Stampacchia type of generalized vector quasivariational-like inequalities for fuzzy mappings was studied under compact assumption using Ky Fan's section theorem [7].

• 호남수학학술지
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• 제27권3호
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• pp.445-463
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• 2005

In this paper, we introduce a Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings and consider the existence of solutions to them under non-compact assumption.

• 대한수학회보
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• 제50권3호
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• pp.777-786
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• 2013

The purpose of this paper is to establish some relationships between proper efficiency of set-valued optimization problems and proper efficiency of vector variational-like inequalities under the assumptions of generalized cone-preinvexity. Our results extend and improve the corresponding results in the literature.

• 대한수학회지
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• 제39권3호
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• pp.397-410
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• 2002

In this paper, some inequalities for vector-valued maximal functions over locally compact Vienkin groups are obtained.

• 대한수학회지
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• 제48권4호
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• pp.703-725
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• 2011

In this paper, we establish the vector-valued inequalities for the commutators of singular integrals with rough kernels. In particular, our results can essentially improve some well-known results.