대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권2호
  • /
  • Pages.389-404
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  • 2023
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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HANKEL DETERMINANTS FOR STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRICAL POINTS

  • Nak Eun Cho (Department of Applied Mathematics Pukyong National University) ;
  • Young Jae Sim (Department of Applied Mathematics Kyungsung University) ;
  • Derek K. Thomas (Department of Mathematics Swansea University Bay Campus)
  • 투고 : 2022.02.23
  • 심사 : 2022.08.01
  • 발행 : 2023.03.31
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초록

We prove sharp bounds for Hankel determinants for starlike functions f with respect to symmetrical points, i.e., f given by $f(z)=z+{\sum{_{n=2}^{\infty}}}\,{\alpha}_nz^n$ for z ∈ 𝔻 satisfying $$Re{\frac{zf^{\prime}(z)}{f(z)-f(-z)}}>0,\;z{\in}{\mathbb{D}}$$. We also give sharp upper and lower bounds when the coefficients of f are real.

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과제정보

The authors would like to express their thanks to the referees for their valuable comments and suggestions. The first named author (N. E. Cho) was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2019R1I1A3A01050861).

참고문헌

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