Radius of strongly starlikeness for certain analytic functions
The authors consider an interesting subclass of analytic and \(p\)-valent functions which are strongly starlike of order \(\gamma(p\in \mathbb{N}: =\{1,2,3,\dots\}\); \(0<\gamma\leq 1)\). In particular, for a normalized analytic and \(p\)-valent function \(f(z)\) in the open unit disk, they put \(F(z)=f(z) [Q(z)]^{\beta/n}\) \((\beta\in \mathbb{R};\;n\in\mathbb{N})\), where \(Q(z)\) is a polynomial of degree \(n\), all of whose zeros lie outside or on the unit circle, and then determine the radius \(R(\gamma)\) such that \(F(z)\) is \((p\)-valently) strongly starlike of order \(\gamma\) in \(|z|< R(\gamma)\).
scientific article; zbMATH DE number 1780341