A study of sharp coefficient bounds for a new subfamily of starlike functions - Ullah, Khalil; Srivastava, H. M.; Rafiq, Ayesha; Arif, Muhammad; Arjika, Sama (Journal of inequalities and applications, 2021)
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.