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

• Published in: Journal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 20
• Main Authors: Ullah, Khalil, Srivastava, H. M., Rafiq, Ayesha, Arif, Muhammad, Arjika, Sama
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 17.12.2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Analytic (or regular or holomorphic) functions; Applications of Mathematics; Coefficients; Estimates; Hyperbolic and trigonometric functions; Hyperbolic functions; Mathematics; Mathematics and Statistics; Principle of subordination; Schwarz function; Starlike functions; Univalent functions; Starlike functions; Analytic (or regular or holomorphic) functions; Schwarz function; Univalent functions; Fekete–Szegö functional; Coefficient bounds; The quantum or basic (or; calculus and its trivial; Principle of subordination; Hyperbolic and trigonometric functions; variation
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-021-02729-1

In this article, by employing the hyperbolic tangent function tanh z , a subfamily S tanh ∗ of starlike functions in the open unit disk D ⊂ C : D = { z : z ∈ C  and  | z | < 1 } 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 ∗ of starlike functions in 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.