• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.517-521
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• 2011

In this paper, we introduce the concepts of m-convex set, mcconvex function and $m^*c$-convex function. We study basic properties for m-convex sets and characterization for such functions.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.277-284
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• 2004

An m-transversal to a family of convex sets in the plane is an m-point set which intersects every members of the family. One of Grubaum's conjectures says that a planar family of translates of a convex compact set has a 3-transversal provided that any two of its members intersect. Recently the conjecture has been proved affirmatively (see [4]). In the present paper we provide a different and straightforward proof for the conjecture for the family of translates of a closed trapezoid in the plane and give several concrete 3-transversals.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.371-378
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• 2010

In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (${\alpha}$, m)-convex.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.669-677
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• 1996

Let $M_n$ be the $C^*$-algebra of all $n \times n$ matrices over the complex field, and $P[M_m, M_n]$ the convex cone of all positive linear maps from $M_m$ into $M_n$ that is, the maps which send the set of positive semidefinite matrices in $M_m$ into the set of positive semi-definite matrices in $M_n$. The convex structures of $P[M_m, M_n]$ are highly complicated even in low dimensions, and several authors [CL, KK, LW, O, R, S, W]have considered the possibility of decomposition of $P[M_m, M_n] into subcones.

• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.307-317
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• 2012

In this paper we establish several Hadamard-type integral inequalities for (${\alpha}$, m)-convex functions.

• Proceedings of the Korea Information Processing Society Conference
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• 2012.11a
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• pp.330-332
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• 2012

본 논문에서는 임의의 정렬되지 않은 평면 점집합(Plane Point Set)에서 정렬을 고려한 개선된 Convex Hull 알고리즘을 제안한다. 이 알고리즘은 Convex Hull의 극점(Extreme Point) 특성을 이용하여 처리 데이터를 한정하기 때문에 계산복잡도를 낮춘다. 각 단계마다 볼록 정점(Convex Vertex)만을 판별하는 조건을 이용하여 한 번의 스캔으로 온전한 Convex Set이 구한다. 알고리즘 초기에 점집합의 정렬이 필요한데, 이때 걸리는 시간이 알고리즘 전체 동작시간의 대부분을 차지하는 만큼, 특성에 맞는 방법을 사용하여 빠르게 정렬하였다. 일반적인 상황을 가정하고 점집합을 랜덤하게 구성하여 실험하였으며 기존의 알고리즘에 비해 약 두 배의 속도 향상이 있음을 확인하였다.

• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.153-162
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• 2001

In this Paper, the notion of $\varepsilon$-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. Mat. 29(1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Approx. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each $\varepsilon$>0 there exists a continuous $\varepsilon$-near best approximation $\phi$ : X → M of X by M then M is a chebyshev set .

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.195-200
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• 2010

Let C be a closed convex set in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$. Assume that ${\Sigma}$ is an n-dimensional compact minimal submanifold outside C such that ${\Sigma}$ is orthogonal to ${\partial}C$ along ${\partial}{\Sigma}{\cap}{\partial}C$ and ${\partial}{\Sigma}$ lies on a geodesic sphere centered at a fixed point $p{\in}{\partial}{\Sigma}{\cap}{\partial}C$ and that r is the distance in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$ from p. We make use of a modified volume $M_p({\Sigma})$ of ${\Sigma}$ and obtain a sharp relative isoperimetric inequality $$\frac{1}{2}n^n{\omega}_nM_p({\Sigma})^{n-1}{\leq}Vol({\partial}{\Sigma}{\sim}{\partial}C)^n$$, where ${\omega}_n$ is the volume of a unit ball in ${\mathbb{R}}^n$ Equality holds if and only if ${\Sigma}$ is a totally geodesic half ball centered at p.

• Structural Engineering and Mechanics
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• v.18 no.4
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• pp.461-474
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• 2004

A proposed incremental model for the solution of a general class of convex programming problems is introduced. The model is an extension of that developed by Mahmoud et al. (1993) which is limited to linear constraints having nonzero free coefficients. In the present model, this limitation is relaxed, and allowed to be zero. The model is extended to accommodate those constraints of zero free coefficients. The proposed model is applied to solve the elasto-static contact problems as a class of variation inequality problems of convex nature. A set of different physical nature verification examples is solved and discussed in this paper.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.66-70
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• 2007

Note that Choquet integral is a generalized concept of Lebesgue integral, because two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure. In this paper, we consider interval-valued Choquet integrals with respect to fuzzy measures(see [4,5,6,7]). Using these Choquet integrals, we define a mappings on the classes of Choquet integrable functions and give an example of a mapping defined by interval-valued Choquet integrals. And we will investigate some relations between m-convex mappings ${\phi}$ on the class of Choquet integrable functions and m-convex mappings $T_{\phi}$, defined by the class of closed set-valued Choquet integrals with respect to fuzzy measures.