Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 171-178.

• Articles • Previous Articles     Next Articles

The Univalent Radius of Harmonic Mappings Under Complex-Operator

 ZHU Jian-Feng, HUANG Xin-Zhong   

  1. School of Mathematical Sciences, Huaqiao University, Fujian Quanzhou 362021
  • Received:2012-06-10 Revised:2013-05-15 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    华侨大学侨办基金资助项目(10QZR22)和国家自然科学基金项目(11101165)资助.

Abstract:

Assume f(z) is a harmonic mapping defined in the unit disk D, denote complex-operator L:=z∂/∂z-z∂/∂z. In this paper, assume f satisfys coefficient condition (1.7), we obtained the univalent radius ρ0 of L(f). Here ρ0 is defined by (1.9). Moreover, if f is a harmonic K-quasiconformal mapping, we also obtained the univalent radium ρK of L(f).

Key words: Harmonic mapping, quasiconformal mapping, Bloch constant, Landau theorem, Complex-operator

CLC Number: 

  • 30C75
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