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 α were introduced and studied from different viewpoints. In this paper, we investigate the relation between various former types of q-starlike functions of order α. We also introduce and study a new subclass of q-starlike functions of order α. 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.