Certain Properties of Some Families of Generalized Starlike Functions with respect to q-Calculus

Abstract

By making use of the concept of $q$-calculus, various types of generalized starlike functions of order $\alpha$ were introduced and studied from different viewpoints. In this paper, we investigate the relation between various former types of $q$-starlike functions of order $\alpha$. We also introduce and study a new subclass of $q$-starlike functions of order $\alpha$. Moreover, we give some properties of those $q$-starlike functions with negative coefficient including the radius of univalency and starlikeness. Some illustrative examples are provided to verify the theoretical results in case of negative coefficient functions class.