• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권2호
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• pp.87-93
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• 1999

A holomorphic function f on D = {z : │z│ ＜ 1} is called uniformly locally univalent if there exists a positive constant $\rho$ such that f is univalent in every hyperbolic disk of hyperbolic radius $\rho$. We establish a characterization of uniformly locally univalent functions and investigate uniform local univalence of holomorphic universal covering projections.

• 충청수학회지
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• 제34권2호
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• pp.139-155
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• 2021

Using a modular transformation formula for a class of functions related to generalized non-holomorphic Eisenstein series, we find a new class of infinite series about identities, some of which include generalized formulae of several Berndt's results.

• 대한수학회보
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• 제20권1호
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• pp.15-25
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• 1983

The main purpose of the present paper is to generalize the results obtained by A. Hindmarsh in [7] to the holomorphic functions with non-negative real part defined on a complete circular domain D in certain class D in the complex euclidean space $C^{n}$. As described in .cint.2, D includes the bounded symmetric domains.s.

• 대한수학회논문집
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• 제33권3호
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• pp.833-851
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• 2018

In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results generalize some of the results of Fang and Zalcman [4] and Chen et al. [2] to a great extent.

• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.155-163
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• 2008

This is an extended version of the paper [K] of the author. The average formulas on the circles and disks around arbitrary points of Nevanlinna counting functions of holomorphic self-maps of the unit disk, given in terms of the boundary values of the selfmaps, are shown to give another characterization of the whole class or a special subclass of inner functions in terms of Nevanlinna counting function in addition to the previous applications to Rudin's orthogonal functions.

• 대한수학회논문집
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• 제11권1호
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• pp.81-87
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• 1996

We will construct polynomials of degree 6 in z and $\bar{z}$ on $C^2$ which gives, via its coefficient $\beta$ as a parameter, a family of pseudoconvex domains $\Omega_\beta$ in $C^2$ with the origin being a boundary point, and show that the domains $\Omega_\beta$ has no peak functions of class $c^1$ at the origin and has no holomorphic support functions for $1 \leq \beta < \frac{9}{5}$.

• East Asian mathematical journal
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• 제31권3호
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• pp.351-356
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• 2015

In this paper, we study holomorphic discs in a domain with a plurisubharmonic peak function at a boundary point. The aim is to describe boundary behavior of holomorphic discs in convex finite type domains in the complex Euclidean space in term of a special local neigh-borhood system at a boundary point.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.219-227
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• 2014

In this note we study the Schwarz lemma and inequalities for some holomorphic functions on the unit disc. Also, we obtain the inequality of the derivative of holomorphic maps at a boundary point of the unit disc and find a holomorphic map to satisfy the equality.

• Korean Journal of Mathematics
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• 제12권2호
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• pp.107-115
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• 2004

In this paper, the new subclass denoted by $S_p({\alpha},{\beta},{\xi},{\gamma})$ of $p$-valent holomorphic functions has been introduced and investigate the several properties of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$. In particular we have obtained integral representation for mappings in the class $S_p({\alpha},{\beta},{\xi},{\gamma})$) and determined closed convex hulls and their extreme points of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$.

• 대한수학회지
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• 제49권2호
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• pp.379-394
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• 2012

Given an almost complex structure ($\mathbb^{C}^m$, J), $m\geq2$, that is defined by setting $\theta^{\alpha}=dz^{\alpha}+a_{\beta}^{\alpha}d\bar{z}^{\beta}$, ${\alpha}=1,\ldots$,m, to be (1, 0)-forms, we find conditions on ($a_{\beta}^{\alpha}$) for the existence of holomorphic functions an classify the almost complex structures by type ($\nu$,q). Then we determine types for several examples in $\mathbb{C}^2$ and $\mathbb{C}^3$ including the natural almost complex structure on $S^6$.