Higher-order q-derivatives and their applications to subclasses of multivalent Janowski type q-starlike functions

Abstract

Abstract In the present investigation, with the help of certain higher-order q-derivatives, some new subclasses of multivalent q-starlike functions which are associated with the Janowski functions are defined. Then, certain interesting results, for example, radius problems and the results related to distortion, are derived. We also derive a sufficient condition and certain coefficient inequalities for our defined function classes. Some known consequences related to this subject are also highlighted. Finally, the well-demonstrated fact about the ( p , q ) $(p,q)$ -variations is also given in the concluding section.

Keywords

• Analytic functions
• Multivalent functions
• q-Difference (or q-Derivative) operator
• q-Starlike functions
• Distortion theorems
• Janowski functions