Kyungpook Mathematical Journal

  • 제61권3호
  • /
  • Pages.513-522
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  • 2021
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On Coefficients of a Certain Subclass of Starlike and Bi-starlike Functions

  • Mahzoon, Hesam (Department of Mathematics, Islamic Azad University) ;
  • Sokol, Janusz (College of Natural Sciences, University of Rzeszow)
  • 투고 : 2019.06.06
  • 심사 : 2020.07.02
  • 발행 : 2021.09.30
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초록

In this paper we investigate a subclass 𝓜(α) of the class of starlike functions in the unit disk |z| < 1. 𝓜(α), π/2 ≤ α < π, is the set of all analytic functions f in the unit disk |z| < 1 with the normalization f(0) = f'(0) - 1 = 0 that satisfy the condition $$1+\frac{{\alpha}-{\pi}}{2\;sin\;{\alpha}}. The class 𝓜(α) was introduced by Kargar et al. [Complex Anal. Oper. Theory 11: 1639-1649, 2017]. In this paper some basic geometric properties of the class 𝓜(α) are investigated. Among others things, coefficients estimates and bound are given for the Fekete-Szegö functional associated with the k-th root transform [f(zk)]1/k. Also a certain subclass of bi-starlike functions is introduced and the bounds for the initial coefficients are obtained.

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참고문헌

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