• Title/Summary/Keyword: Univalent harmonic functions

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Partial Sums of Starlike Harmonic Univalent Functions

  • Porwal, Saurabh;Dixit, Kaushal Kishore
    • Kyungpook Mathematical Journal
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    • v.50 no.3
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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.

CONSTRUCTION OF SUBCLASSES OF UNIVALENT HARMONIC MAPPINGS

  • Nagpal, Sumit;Ravichandran, V.
    • Journal of the Korean Mathematical Society
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    • v.51 no.3
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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.

SOME INCLUSION RELATIONS OF CERTAIN SUBCLASSES OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH GENERALIZED DISTRIBUTION SERIES

  • Magesh, Nanjundan;Porwal, Saurabh;Themangani, Rajavadivelu
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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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.

Some Properties of Harmonic Functions Defined by Convolution

  • Dixit, Kaushal Kishor;Porwal, Saurabh
    • Kyungpook Mathematical Journal
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    • v.49 no.4
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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.

UNIVALENT FUNCTIONS ON Δ = {z : |z| > 1}

  • Jun, Sook Heui
    • Korean Journal of Mathematics
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    • v.11 no.2
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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 ${\mid}z{\mid}=1$.

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MEROMOR0PHIC UNIVALENT HARMONIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Jahangiri, Jay M.;Silverman, Herb
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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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.

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UNIVALENT HARMONIC EXTERIOR MAPPINGS

  • Jun, Sook Heui
    • Journal of the Chungcheong Mathematical Society
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    • v.16 no.2
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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.

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