• 호남수학학술지
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• 제42권4호
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• pp.701-717
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• 2020

We introduced and studied a new class of harmonic univalent functions on unit disc 𝕌. Also we provided coefficient conditions, extreme points and convolution conditions for that class of harmonic univalent functions.

• Kyungpook Mathematical Journal
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• 제50권3호
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• pp.433-445
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• 2010

Although, interesting properties on the partial sums of analytic univalent functions have been investigated extensively by several researchers, yet analogous results on partial sums of harmonic univalent functions have not been so far explored. The main purpose of the present paper is to establish some new and interesting results on the ratio of starlike harmonic univalent function to its sequences of partial sums.

• 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.

• 대한수학회논문집
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• 제35권3호
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• pp.843-854
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• 2020

The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.751-761
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• 2009

In this paper, we introduce and study a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Also, we improve some results obtained by Frasin [3] and obtain coefficient bounds, distortion bounds and extreme points, convolution conditions and convex combination are also determined for functions in this family. It is worth mentioning that many of our results are either extensions or new approaches to those corresponding previously known results.

• 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 ${\mid}z{\mid}=1$.

• 대한수학회지
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• 제43권4호
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• pp.803-813
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• 2006

We define and investigate a subclass of complex valued harmonic convex functions that are univalent and sense preserving in the open unit disk. We obtain coefficient conditions, extreme points, distortion bounds, convolution conditions for the above family of harmonic functions.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.83-89
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• 2015

In the present paper, we introduce new subclasses of harmonic univalent functions and establish certain results concerning the convolution of functions for these subclasses. Relevant connections of the results presented here with various known results are briefly indicated.

• 대한수학회보
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• 제36권4호
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• pp.763-770
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• 1999

The purpose of this paper is to give sufficient coefficient conditions for a class of univalent harmonic functions that map each $$\mid$z$\mid$$ = r >1 onto a curve that bounds a domain that is starlike with respect to origin. Furthermore, it is shown that these conditions are also necessary when the coefficients are negative. Extreme points for these classes are also determined. Finally, comparable results are given for the convex analgo.

• 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.