A study of sharp coefficient bounds for a new subfamily of starlike functions

Journal of Inequalities and Applications

Sama Arjika¹  H. M. Srivastava²  Muhammad Arif³  Khalil Ullah³  Ayesha Rafiq⁴ 

[1] Department of Mathematics and Informatics, University of Agadez;Department of Mathematics and Statistics, University of Victoria;Department of Mathematics, Abdul Wali khan University;Institute of Space Technology, University of Islamabad;

关键词: Analytic (or regular or holomorphic) functions;    Univalent functions;    Starlike functions;    Principle of subordination;    Schwarz function;    Hyperbolic and trigonometric functions;   

DOI  :  10.1186/s13660-021-02729-1

来源: DOAJ

【 摘 要 】

Abstract In this article, by employing the hyperbolic tangent function tanhz, a subfamily S tanh ∗ $\mathcal{S}_{\tanh }^{\ast }$ of starlike functions in the open unit disk D ⊂ C $\mathbb{D}\subset \mathbb{C}$ : D = { z : z ∈ C  and  | z | < 1 } $$\begin{aligned} \mathbb{D}= \bigl\{ z:z\in \mathbb{C} \text{ and } \vert z \vert < 1 \bigr\} \end{aligned}$$ is introduced and investigated. The main contribution of this article includes derivations of sharp inequalities involving the Taylor–Maclaurin coefficients for functions belonging to the class S tanh ∗ $\mathcal{S}_{\tanh }^{\ast } $ of starlike functions in D $\mathbb{D}$ . In particular, the bounds of the first three Taylor–Maclaurin coefficients, the estimates of the Fekete–Szegö type functionals, and the estimates of the second- and third-order Hankel determinants are the main problems that are proposed to be studied here.

【 授权许可】

Unknown