• 충청수학회지
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• 제20권4호
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• pp.349-353
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• 2007

In this paper, we obtain some coefficient bounds of harmonic univalent mappings by using properties of the analytic univalent function on ${\Delta}$={z : |z| > 1}.

• 충청수학회지
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• 제22권4호
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• pp.749-756
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• 2009

In this paper, we obtain some coefficient bounds of harmonic univalent mappings on $\Delta=\{z\;:\;{\mid}z{\mid}\;>\;1\}$ which are starlike, convex, or convex in one direction.

• 대한수학회지
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• 제51권3호
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• pp.567-592
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• 2014

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are introduced and their properties are investigated.

• Korean Journal of Mathematics
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• 제15권2호
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• pp.171-176
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• 2007

The purpose of this paper is to study harmonic univalent mappings defined in ${\Delta}=\{z:{\mid}z{\mid}>1\}$ that map ${\infty}$ to ${\infty}$. Some coefficient estimates are obtained in a normalized class of mappings.

• Korean Journal of Mathematics
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• 제11권2호
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• pp.79-84
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• 2003

In this paper, we obtain the sharp estimates for co-efficients of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$ when harmonic mappings are of bounded variation on ${\mid}z{\mid}=1$.

• 충청수학회지
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• 제16권2호
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• pp.31-41
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• 2003

In this paper, we will show that the bounds for coefficients of harmonic, orientation-preserving, univalent mappings f defined on ${\Delta}$ = {z : |z| > 1} with $f({\Delta})={\Delta}$ are sharp by finding extremal functions.

• 충청수학회지
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• 제17권2호
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• pp.163-167
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• 2004

In this paper, we obtain some coefficient estimates of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}$ = {z : |z| > 1}.

• 대한수학회보
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• 제51권3호
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• pp.803-812
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• 2014

Let ${\mathcal{S}}^0_{\mathcal{H}}$ be the class of normalized univalent harmonic mappings in the unit disk. A subclass ${\mathcal{V}}^{\mathcal{H}}(k)$ of ${\mathcal{S}}^0_{\mathcal{H}}$, whose analytic part is function with bounded boundary rotation, is introduced. Some bounds for functionals, specially harmonic pre-Schwarzian derivative, described in ${\mathcal{V}}^{\mathcal{H}}(k)$ are given.

• Korean Journal of Mathematics
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• 제10권1호
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• pp.1-3
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• 2002

In this paper, we obtain some coefficient bounds of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$.

• 대한수학회지
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• 제32권4호
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• pp.803-814
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• 1995

Let $\Sigma$ be the class of all complex-valued, harmonic, orientation-preserving, univalent mappings defined on $\Delta = {z : $\mid$z$\mid$ > 1}$ that map $\infty$ to $\infty$.