Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Coefficient Bounds for a Subclass of Harmonic Mappings Convex in One Direction

  • Shabani, Mohammad Mehdi (Department of Mathematics, University of Shahrood) ;
  • Yazdi, Maryam (Young Researchers and Elite Club, Malard Branch, Islamic Azad University) ;
  • Sababe, Saeed Hashemi (Department of Mathematical and Statistical Sciences, University of Alberta, Young Researchers and Elite Club, Malard Branch, Islamic Azad University)
  • Received : 2020.08.06
  • Accepted : 2020.12.14
  • Published : 2021.06.30
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Abstract

In this paper, we investigate harmonic univalent functions convex in the direction 𝜃, for 𝜃 ∈ [0, 𝜋). We find bounds for |fz(z)|, ${\mid}f_{\bar{z}}(z){\mid}$ and |f(z)|, as well as coefficient bounds on the series expansion of functions convex in a given direction.

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Acknowledgement

The authors thanks to the referee, especially for his comment on Corollary 3.3. A part of this research was carried out while the third author was visiting the university of Alberta. The author is grateful to his colleagues in the department of mathematical and statistical siecnces for their kind hosting.

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