• 제목/요약/키워드: harmonic starlike

검색결과 14건 처리시간 0.031초

QUASICONFORMAL EXTENSIONS OF STARLIKE HARMONIC MAPPINGS IN THE UNIT DISC

  • Hamada, Hidetaka;Honda, Tatsuhiro;Shon, Kwang Ho
    • 대한수학회보
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    • 제50권4호
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    • pp.1377-1387
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    • 2013
  • Let $f$ be a harmonic mapping on the unit disc ${\Delta}$ in $\mathbb{C}$. We give some condition for $f$ to be a quasiconformal homeomorphism on ${\Delta}$ and to have a quasiconformal extension to the whole plane $\bar{\mathbb{C}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order ${\alpha}{\in}(0,1)$.

Partial Sums of Starlike Harmonic Univalent Functions

  • Porwal, Saurabh;Dixit, Kaushal Kishore
    • 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.

HARMONIC MEROMORPHIC STARLIKE FUNCTIONS

  • Jahangiri, Jay, M.
    • 대한수학회보
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    • 제37권2호
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    • pp.291-301
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    • 2000
  • We give sufficient coefficient conditions for a class of meromorphic univalent harmonic functions that are starlike of some order. Furthermore, it is shown that these conditions are also necessary when the coefficients of the analytic part of the function are positive and the coefficients of the co-analytic part of the function are negative. Extreme points, convolution and convex combination conditions for these classes are also determined. Fianlly, comparable results are given for the convex analogue.

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

  • Magesh, Nanjundan;Porwal, Saurabh;Themangani, Rajavadivelu
    • 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.

Multivalent Harmonic Uniformly Starlike Functions

  • Ahuja, Om;Joshi, Santosh;Sangle, Naveneet
    • Kyungpook Mathematical Journal
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    • 제49권3호
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    • pp.545-555
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    • 2009
  • In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.

MEROMOR0PHIC UNIVALENT HARMONIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Jahangiri, Jay M.;Silverman, Herb
    • 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.

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STUDY ON UNIVALENT HARMONIC MAPPINGS

  • Jun, Sook Heui
    • 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.

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New Subclasses of Harmonic Starlike and Convex Functions

  • Porwal, Saurabh;Dixit, Kaushal Kishore
    • Kyungpook Mathematical Journal
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    • 제53권3호
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    • pp.467-478
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    • 2013
  • The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes $V_H({\beta})$ and $U_H({\beta})$. Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.

CONSTRUCTION OF SUBCLASSES OF UNIVALENT HARMONIC MAPPINGS

  • Nagpal, Sumit;Ravichandran, V.
    • 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.