数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (4): 1244-1270.doi: 10.1007/s10473-024-0404-8

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STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION

Mohsan Raza1, Hadiqa Zahid1, Jinlin Liu2,*   

  1. 1. Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan;
    2. Department of Information Science, Yangzhou University, Yangzhou 225002, China
  • 收稿日期:2022-12-27 修回日期:2023-04-11 出版日期:2024-08-25 发布日期:2024-08-30

STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION

Mohsan Raza1, Hadiqa Zahid1, Jinlin Liu2,*   

  1. 1. Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan;
    2. Department of Information Science, Yangzhou University, Yangzhou 225002, China
  • Received:2022-12-27 Revised:2023-04-11 Online:2024-08-25 Published:2024-08-30
  • Contact: *E-mail: jlliu@yzu.edu.cn
  • About author:E-mail: mohsan976@yahoo.com; hadiqazahid219@gmail.com
  • Supported by:
    The first author's work was supported by the Grant No. 20-16367/NRPU/RD/HEC/2021 2021.

摘要: Let qλ(z)=1+λsinh(ζ), 0<λ<1/sinh(1) be a non-vanishing analytic function in the open unit disk. We introduce a subclass S(qλ) of starlike functions which contains the functions f such that zf/f is subordinated by qλ. We establish inclusion and radii results for the class S(qλ) for several known classes of starlike functions. Furthermore, we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S(qλ). We also find a sharp bound for the third Hankel determinant for the case λ=1/2.

关键词: starlike functions, sine hyperbolic functions, radii problems, coefficient bounds, Hankel determinants

Abstract: Let qλ(z)=1+λsinh(ζ), 0<λ<1/sinh(1) be a non-vanishing analytic function in the open unit disk. We introduce a subclass S(qλ) of starlike functions which contains the functions f such that zf/f is subordinated by qλ. We establish inclusion and radii results for the class S(qλ) for several known classes of starlike functions. Furthermore, we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S(qλ). We also find a sharp bound for the third Hankel determinant for the case λ=1/2.

Key words: starlike functions, sine hyperbolic functions, radii problems, coefficient bounds, Hankel determinants

中图分类号: 

  • 30C45