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

الملخص EN

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.