• Korean Journal of Mathematics
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• v.7 no.1
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• pp.85-101
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• 1999

Let $p$ be analytic in the unit disc U and let $q$ be univalent in U. In addition, let ${\Omega}$ be a set in C and let ${\psi}:c^3{\times}U{\rightarrow}C$. The author determines conditions on ${\psi}$ so that $$\{{\psi}(p(z),zp^{\prime}(z),z^2p^{{\prime}{\prime}}(z);z){\mid}z{\in}U\}{\subset}{\Omega}{\Rightarrow}p(U){\subset}q(U)$$. Applications of this result to differential inequalities, differential subordinations and integral inequalities are presented.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.451-463
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• 2015

A continuous and non-decreasing function ${\psi}$ and another continuous function ${\phi}$ with ${\phi}(z)=0{\Leftrightarrow}z=0$ defined on $\mathbb{C}^+=\{x+yi:x,y{\geq}0\}$ are introduced, the ${\psi}-{\phi}$-contractive or expansive type conditions are considered, and the existence theorems of common fixed points for two mappings defined on a complex valued metric space are obtained. Also, Banach contraction principle and a fixed point theorem for a I-expansive type mapping are given on complex valued metric spaces.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.593-605
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• 2017

In this paper, we consider some normality criteria concerning multiple values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain D. Let k be a positive integer and ${\psi}(z){\not\equiv}0$, ${\infty}$ be a meromorphic function in D. If, for each $f{\in}\mathcal{F}$ and $z{\in}D$, (1) $f(z){\neq}0$, and all of whose poles are multiple; (2) all zeros of $f^{(k)}(z)-{\psi}(z)$ have multiplicities at least k + 3 in D; (3) all poles of ${\psi}(z)$ have multiplicities at most k in D, then $\mathcal{F}$ is normal in D.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.113-119
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• 2010

If f is M-harmonic and integrable with respect to a weighted radial measure $\upsilon_{\alpha}$ over the unit ball $B_n$ of $\mathbb{C}^n$, then $\int_{B_n}(f\circ\psi)d\upsilon_{\alpha}=f(\psi(0))$ for every $\psi{\in}Aut(B_n)$. Equivalently f is fixed by the weighted Berezin transform; $T_{\alpha}f = f$. In this paper, we show that if a function f defined on $B_n$ satisfies $R(f\circ\phi){\in}L^{\infty}(B_n)$ for every $\phi{\in}Aut(B_n)$ and Sf = rf for some |r|=1, where S is any convex combination of the iterations of $T_{\alpha}$'s, then f is M-harmonic.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.203-210
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• 1997

We give some interesting identities involving the Hurwitz and Riemann zeta functions.

• Journal of Korean Society of Forest Science
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• v.101 no.3
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• pp.461-468
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• 2012

This study was conducted to study the seasonal changes of relative water relations parameters by pressure-volume curves of Korean mistletoe (Viscum album var. coloratum) leaves for understanding ecological characteristics. In growing season, the osmotic potentials at full turgor (${\Psi}_o^{sat}$) and at incipient plasmolysis (${\Psi}_o^{tlp}$) decreased, while increased the maximum bulk elastic modulus of the cell wall ($E_{max}$) and relavive water content ($RWC^{tlp}$). Korean mistletoe in Quercus variabilis and Korean mistletoe in Quercus mongolica in November showed best maximum perssure potential (${\Psi}_{P,\;max}$). Pressure potential (${\Psi}_P$) and water potential (${\Psi}_L$) in Korean mistletoe in Quercus variabilis were rapidly decreased with decreasing of relative water content. The values of $RWC^{tlp}$ in November were all above 84% showing that the function of osmoregulation is somewhat better, and symplastic water content (Vo/DW) and maximum water content (Vt/DW) were variable seasonally. Thus, responses to water relations of Korean mistletoe in Quercus variabilis and Korean mistletoe in Quercus mongolica such as ${\Psi}_o^{sat},\;{\Psi}_o^{tlp},\;E_{max},\;{\Psi}_{P,\;max},\;RWC^{tlp}$ showed increaing drought tolerance with increasing of leaf aging.

• Journal of Korean Ophthalmic Optics Society
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• v.10 no.4
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• pp.273-281
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• 2005

The weight of spectacles fined on is resolved into its components along the nose's slide plane and the normal to the nose plane where the nosepad is located. The equation and its numerical solution to determine the component force was derived as a function of splay angle ${\Psi}$, $sin{\Psi}$, $cos{\Psi}$, and $cot{\Psi}$, incorporated with ${\theta}$ and ${\Phi}$, the angles viewed from side and front of the face, respectively. Values of inclination angle ${\theta}$ and ${\Phi}$ could be obtained to fulfill the condition where the frictional force between the nose and pad is either greater than the normal pressure exerted by the spectacles on the nose. With the value of ${\theta}$ fixed the normal pressure increases as ${\Phi}$ increases. With ${\Phi}$ fixed, the effect of ${\theta}$ is the same.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.417-430
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• 2013

Let X be a Banach space and ${\psi}$ a continuous convex function on ${\Delta}_{K+1}$ satisfying certain conditions. Let $(X{\bigoplus}X{\bigoplus}{\cdots}{\bigoplus}X)_{\psi}$ be the ${\psi}$-direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non-$l^N_1$-ness of Banach spaces using ${\psi}$-direct sums.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.29-38
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• 2017

The main objective of this paper is to establish certain unified integral formula involving the product of the generalized Mittag-Leffler type function $E^{({\gamma}_j),(l_j)}_{({\rho}_j),{\lambda}}[z_1,{\ldots},z_r]$ and the Srivastava's polynomials $S^m_n[x]$. We also show how the main result here is general by demonstrating some interesting special cases.

• Korean Journal of Medicinal Crop Science
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• v.20 no.1
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• pp.36-41
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• 2012

This study was carried out to establish a proper cultivation site and diagnose the drought tolerance of Pleurospermum camtschaticum, Cirsium setidens and Parasenecio firmus leaves by using pressure-volume curves. The result of ${\Psi}_o^{sat}$ and ${\Psi}_o^{tlp}$ were lower in Pleurospermum camtschaticum leaves. On the other hand, it appeared that $E_{max}$ of Pleurospermum camtschaticum was approximately six times higher than that of Parasenecio firmus. The values of $RWC^{tlp}$ is all above 88% showing that the function of osmoregulation is somewhat better, and Vo/DW, Vt/DW, Ns/DW of Pleurospermum camtschaticum leaves were approximately 2~4 times Lower than other ones. Thus, responses to water relations of Pleurospermum camtschaticum, Cirsium setidens and Parasenecio firmus such as ${\Psi}_o^{sat}$, ${\Psi}_o^{tlp}$, $E_{max}$, ${\Psi}_{P,max}$, $RWC^{tlp}$ were shown that the Pleurospermum camtschaticum leave was higher drought tolerance than Cirsium setidens and Parasenecio firmus leaves.