The Properties of Meromorphic Multivalent <i>q</i>-Starlike Functions in the Janowski Domain

Abstract

Many researchers have defined the q-analogous of differential and integral operators for analytic functions using the concept of quantum calculus in the geometric function theory. In this study, we conduct a comprehensive investigation to identify the uses of the Sălăgean q-differential operator for meromorphic multivalent functions. Many features of functions that belong to geometrically defined classes have been extensively studied using differential operators based on q-calculus operator theory. In this research, we extended the idea of the q-analogous of the Sălăgean differential operator for meromorphic multivalent functions using the fundamental ideas of q-calculus. With the help of this operator, we extend the family of Janowski functions by adding two new subclasses of meromorphic q-starlike and meromorphic multivalent q-starlike functions. We discover significant findings for these new classes, including the radius of starlikeness, partial sums, distortion theorems, and coefficient estimates.

Keywords

• quantum (or <i>q</i>-) calculus
• <i>q</i>-derivative operator
• Sălăgean <i>q</i>-differential operator
• meromorphic multivalent <i>q</i>-starlike functions
• Janowski functions