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

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