数学季刊 ›› 2012, Vol. 27 ›› Issue (2): 286-292.

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一类新的单叶调和函数

  

  1. Department of Mathematics, Chifeng College

  • 收稿日期:2010-11-15 出版日期:2012-06-30 发布日期:2023-03-30
  • 作者简介:LI Shu-hai(1966-), male, native of Chifeng, Inner Mongolia, a professor of Chifeng College, engages in geometric function theory and applications; MA Li-na(1982-), female, native of Chifeng, Inner Mongolia, a lecturer of Chifeng College, engages in harmonic analysis.
  • 基金资助:
    Supported by the Natural Science Foundation of Inner Mongolia(2009MS0113); Supported by the Higher School Research Foundation of Inner Mongolia(NJzy08150)

A New Class of Harmonic Univalent Functions

  1. Department of Mathematics, Chifeng College

  • Received:2010-11-15 Online:2012-06-30 Published:2023-03-30
  • About author:LI Shu-hai(1966-), male, native of Chifeng, Inner Mongolia, a professor of Chifeng College, engages in geometric function theory and applications; MA Li-na(1982-), female, native of Chifeng, Inner Mongolia, a lecturer of Chifeng College, engages in harmonic analysis.
  • Supported by:
    Supported by the Natural Science Foundation of Inner Mongolia(2009MS0113); Supported by the Higher School Research Foundation of Inner Mongolia(NJzy08150)

摘要: A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g, where h and g are analytic in U. We define and investigate a new class LHλ(α,β) by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class LHλ(α,β). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points. 

关键词: harmonic function, Salagean operator, extreme points, distortion bounds

Abstract: A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g, where h and g are analytic in U. We define and investigate a new class LHλ(α,β) by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class LHλ(α,β). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points. 

Key words: harmonic function, Salagean operator, extreme points, distortion bounds

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