• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.06a
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• pp.265-266
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• 2007

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.845-859
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• 2016

In this paper, some Hermite-Hadamard-$Fej{\acute{e}}r$ type integral inequalities for harmonically quasi-convex functions in fractional integral forms have been obtained.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.131-137
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• 2006

The object of the present paper is to obtain new conditions for analytic function to be strongly starlike and strongly convex function defined in the open unit disk.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.21-36
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• 2000

In this article we study the relation between subinvariant submean and normal structure in a locally convex topological vector space. This extends in a natural way a result obtained recently by Lau and Takahashi. Our approach also follows closely theirs.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.929-937
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• 2019

The main purpose of this paper is to establish $H{\ddot{o}}lder$ estimates for the Cauchy transform in a class of finite/infinite type convex domains in $\mathbb{C}^2$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.877-884
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• 2021

We prove that if a compact convex hypersurface of ℝⁿ⁺¹ has almost maximal extinction time when it is evolved by the mean curvature flow, then it must be nearly round in the C⁰-norm.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.629-633
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• 2010

In this paper we provide a sharp lower bound of the first Neumann eigenvalue of a compact hypersurface $\Sigma$ inside a convex set C in a Riemannian manifold under the assumption that ${\partial}{\Sigma}$ meets ${\partial}C$ orthogonally.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.413-428
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• 2012

Every contingent claim is unable to be replicated in the incomplete markets. Shortfall risk is considered with some risk exposure. We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where$\tilde{\psi}H$ is a randomized test in the static problem. Convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used as risk measure. It can be shown that we have the same results as in [21, 22] even though convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used. In this paper, we use Fenchel duality Theorem in the literature to deduce necessary and sufficient optimality conditions for the static optimization problem using convex duality methods.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.175-184
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• 2013

In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane $\mathbb{R}^2$ are investigated. The Minkowski mixed convex set of two convex sets K and L is studied and some new geometric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style inequalities for convex domain K are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema ([5]) and Pleijel ([22]).

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.625-639
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• 1996

A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.