English

On The Coefficient Conjecture of Clunie and Sheil-Small

Complex Variables 2019-03-01 v1

Abstract

In this paper, we first prove relation between analytic and co-analytic part of the class harmonic univalent functions S_H(S):={f = h+\overline g|h is element of S} by means of second dilatation is constant. Next, we verify the coefficient conjecture of Clunie and Sheil-Small for class of harmonic univalent functions. Finally, we obtain distortion bounds of this class.

Keywords

Cite

@article{arxiv.1902.11225,
  title  = {On The Coefficient Conjecture of Clunie and Sheil-Small},
  author = {Yaşar Polatoğlu and Oya Mert and Asena Çetinkaya},
  journal= {arXiv preprint arXiv:1902.11225},
  year   = {2019}
}