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 $q_{\lambda }\left( z\right) =1+\lambda \sinh (\zeta ),\ 0<\lambda <1/\sinh \left( 1\right) $ be a non-vanishing analytic function in the open unit disk. We introduce a subclass $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $ of starlike functions which contains the functions $\mathfrak{f}$ such that $z\mathfrak{f}^{\prime }/\mathfrak{f}$ is subordinated by $q_{\lambda }$. We establish inclusion and radii results for the class $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $ for several known classes of starlike functions. Furthermore, we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $. We also find a sharp bound for the third Hankel determinant for the case $\lambda =1/2$.

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

Abstract: Let $q_{\lambda }\left( z\right) =1+\lambda \sinh (\zeta ),\ 0<\lambda <1/\sinh \left( 1\right) $ be a non-vanishing analytic function in the open unit disk. We introduce a subclass $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $ of starlike functions which contains the functions $\mathfrak{f}$ such that $z\mathfrak{f}^{\prime }/\mathfrak{f}$ is subordinated by $q_{\lambda }$. We establish inclusion and radii results for the class $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $ for several known classes of starlike functions. Furthermore, we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $. We also find a sharp bound for the third Hankel determinant for the case $\lambda =1/2$.

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

中图分类号: 

  • 30C45