A note on a subclass of bazilevič functions

Abstract

In this artcle, we introduce and investigate a subclass of Bazilevi{č} functions, denoted by ${\mathcal{B}}_{{\phi }_{A,B}}({\alpha }^{(m)})$. We determine the Hardy space to which this subclass of Bazilevi{č} functions belong to. Additionally, we provide a necessary condition for a particular case of this subclass. Finally, we obtain a sharp coefficient estimate for the functions associated with ${\mathcal{B}}_1(\alpha ).$