Some radius problems related to a certain subclass of analytic functions

Abstract

For real parameters α and β such that 0 ≤ α < 1 < β, we denote by S(α, β) the class of normalized analytic functions which satisfy the following two-sided inequality: $$\alpha < \Re \left( {\frac{{zf'(z)}} {{f(z)}}} \right) < \beta ,z \in \mathbb{U} $$ where \(\mathbb{U}\) denotes the open unit disk. We find a sufficient condition for functions to be in the class S(α, β) and solve several radius problems related to other well-known function classes.