• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.573-583
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• 2005

For a certain set G in the complex plane, we construct a transcendental entire function f whose translated family ${f(2^{n}z)}$ is normal only at z in G and establish the relation between the normal family and the Julia direction of f(z).

• Honam Mathematical Journal
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• v.30 no.2
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• pp.207-217
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• 2008

Digital geometry has strongly contributed to the study of a discrete topological space $X{\subset}{\mathbf{Z}}^n$ with k-adjacency of ${\mathbf{Z}}^n$. As a survey-type article, we review various utilities of digital geometry.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.527-540
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• 2010

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.801-811
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• 1996

Let $Z^d$ denote the set of all d-tuples of integers$(d \geq 1, a positive integer)$. The points in $Z^d$ will be denoted by $\underline{m},\underline{n}$, etc., or sometime, when necessary, more explicitly by $(m_1, m_2, \cdots, m_d)$, $(n_1, n_2, \cdots, n_d)$ etc. $Z^d$ is partially ordered by stipulating $\underline{m} \underline{<}\underline{n} iff m_i \leq n_i$ for each i, $1 \leq i \leq d$.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.119-126
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• 2002

For a stationary multivariate linear process of the form X$_{t}$ = (equation omitted), where {Z$_{t}$ : t = 0$\pm$1$\pm$2ㆍㆍㆍ} is a sequence of stationary linearly positive quadrant dependent m-dimensional random vectors with E(Z$_{t}$) = O and E∥Z$_{t}$∥ $^2$< $\infty$, we prove a central limit theorem.theorem.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.377-386
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• 2008

In this paper, we prove the stability of a Cauchy-Jensen functional equation $$2f(x+y,\;\frac{z+w}2)$$=f(x, z)+f(x, w)+f(y, z)+f(y, w) in the sense of Th. M. Rassias.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.549-554
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• 2014

We present a smooth simply connected closed eight dimensional manifold with distinct symplectic deformation equivalence classes [[${\omega}_i$]], i = 1, 2 such that the symplectic Z invariant, which is defined in terms of the scalar curvatures of almost K$\ddot{a}$hler metrics in [5], satisfies $Z(M,[[{\omega}_1]])={\infty}$ and $Z(M,[[{\omega}_2]])$ < 0.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.499-507
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• 2006

In this paper, we obtain the general solution and the stability of the hi-Jensen functional equation $$4f(\frac {x+y} 2,\;\frac {z+w} 2)=f(x,\;z)+f(x,\;w)+f(y,\;z)+f(y,\;w)$$.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.211-217
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• 2012

In this paper, we give the weighted Lebesgue-Radon-Nikodym theorem with respect to $p$-adic invariant integral on $\mathbb{Z}_p$.

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.231-247
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• 2010

In this paper, we investigate the generalized Hyers-Ulam stability of a bi-Jensen functional equation $4f(\frac{x\;+\;y}{2},\;\frac{z\;+\;w}{2})$ = f(x, z) + f(x, w) + f(y, z) + f(y, w). Also, we establish improved results for the stability of a bi-Jensen equation on the punctured domain.