Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Bohr's Phenomenon for Some Univalent Harmonic Functions

  • Singla, Chinu (Department of Mathematics, Sant Longowal Institute of Engineering and Technology) ;
  • Gupta, Sushma (Department of Mathematics, Sant Longowal Institute of Engineering and Technology) ;
  • Singh, Sukhjit (Department of Mathematics, Sant Longowal Institute of Engineering and Technology)
  • Received : 2021.05.21
  • Accepted : 2021.10.07
  • Published : 2022.06.30
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Abstract

In 1914, Bohr proved that there is an r0 ∈ (0, 1) such that if a power series ∑∞m=0 cmzm is convergent in the open unit disc and |∑∞m=0 cmzm| < 1 then, ∑∞m=0 |cmzm| < 1 for |z| < r0. The largest value of such r0 is called the Bohr radius. In this article, we find Bohr radius for some univalent harmonic mappings having different dilatations. We also compute the Bohr radius for functions that are convex in one direction.

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Acknowledgement

This work was supported by UGC - CSIR, New Delhi in the form of Senior Research Fellowship vide Award Letter Number - 2061540842.

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