A Study of Some Families of Multivalent <i>q</i>-Starlike Functions Involving Higher-Order <i>q</i>-Derivatives

Abstract

In the present investigation, by using certain higher-order q-derivatives, the authors introduce and investigate several new subclasses of the family of multivalent q-starlike functions in the open unit disk. For each of these newly-defined function classes, several interesting properties and characteristics are systematically derived. These properties and characteristics include (for example) distortion theorems and radius problems. A number of coefficient inequalities and a sufficient condition for functions belonging to the subclasses studied here are also discussed. Relevant connections of the various results presented in this investigation with those in earlier works on this subject are also pointed out.

Keywords

• multivalent functions
• <i>q</i>-difference (or <i>q</i>-derivative) operator
• distortion theorems
• radius problem