• 한국지능시스템학회논문지
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• 제19권3호
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• pp.421-424
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• 2009

Fuzzy semi-weakly r-semicontinuous 함수의 개념을 소개하며 특성을 조사한다. 본 논문에서 소개된 함수와 fuzzy r-semicontinuity와 fuzzy weakly r-semicontinuity의 관계를 밝힌다.

• 대한수학회보
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• 제52권6호
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• pp.1777-1795
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• 2015

In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition ($H_h$(${\gamma}_0$, ${\lambda}_0$, ${\mu}_0$)) is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1419-1430
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• 2010

Since Goetschel and Voxman [5] proposed a linear order on fuzzy numbers, several authors studied the concept of semicontinuity and convexity of fuzzy mappings defined through the order. Since the order is only defined for fuzzy numbers on $\mathbb{R}$, it is natural to find a new order for normal fuzzy sets on $\mathbb{R}^n$ in order to study the concept of semicontinuity and convexity of fuzzy mappings on normal fuzzy sets. In this paper, we introduce a new order "${\preceq}_s$ for normal fuzzy sets on $\mathbb{R}^n$ with respect to the support function. We define the semicontinuity and convexity of fuzzy mappings with this order. Some issues which are related with semicontinuity and convexity of fuzzy mappings will be discussed.

• 대한수학회보
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• 제34권3호
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• pp.447-457
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• 1997

Let A be a $C^*$-algebra and $A^**$ its enveloping von Neumann algebra. Pedersen and Akemann developed four concepts of lower semicontinuity for elements of $A^**$. Later, Brown suggested using only three classes: strongly lsc, middle lsc, and weakly lsc. In this paper, we generalize the concept of weak semicontinuity [1, 3] to the case of unbounded operators affiliated with $A^**$. Also we consider the generalized version of the conditions of the Brown's theorem [3, Proposition 2.2 & 3.27] for unbounded operators.

• 대한수학회지
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• 제37권5호
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• pp.849-856
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• 2000

We give a new saddle point theorem for vector-valued functions on an admissible compact convex set in a topological vector space under weak condition that is the semicontinuity of two function scalarization and acyclicty of the involved sets. As application, we obtain the minimax theorem.

• 대한수학회보
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• 제52권4호
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• pp.1321-1325
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• 2015

In this paper we study the semicontinuity of the automorphism groups of domains in multi-dimensional complex space. We give examples to show that known results are sharp (in terms of the required boundary smoothness).

• 충청수학회지
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• 제23권2호
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• pp.223-229
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• 2010

We introduce the notion of weak M-semicontinuity which is a generalization of M-semicontinuity defined between spaces with minimal structures. We also investigate some properties and characterizations for such a notion.

• 대한수학회지
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• 제52권6호
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• pp.1149-1159
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• 2015

This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $$-{\Delta}u_t+{\alpha}^2{\Delta}^2u_t+{\mu}{\Delta}^2u+{\bigtriangledown}{\cdot}{\vec{F}}(u)+B(u,u)={\epsilon}g(x,t)$$. Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor $\{A_{\epsilon}(t)\}_{t{\epsilon}{\mathbb{R}}}$ of the equation with ${\epsilon}>0$ converges to the global attractor A of the equation with ${\epsilon}=0$.

• 대한수학회논문집
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• 제24권3호
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• pp.425-432
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• 2009

This paper introduces a local non-positivity of two set-valued mappings (F,Q) and considers the existences and properties of solutions for set-valued mixed vector FQ-implicit variational inequality problems and set-valued mixed vector FQ-complementarity problems in the neighborhood of a point belonging to an underlined domain K of the set-valued mappings, where the neighborhood is contained in K. This paper generalizes and extends many results in [1, 3-7].

• 호남수학학술지
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• 제31권2호
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• pp.247-258
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• 2009

This paper introduces new mixed vector FQ-implicit variational inequality problems and corresponding mixed vector FQ-implicit complementarity problems for set-valued mappings, and studies the equivalence between them under certain assumptions in Banach spaces. It also derives some new existence theorems of solutions for them with examples under suitable assumptions without monotonicity. This paper generalizes and extends many results in [8, 10, 19-22].