Fractal Fract, Vol. 7, Pages 438: The Properties of Meromorphic Multivalent q-Starlike Functions in the Janowski Domain

Fractal Fract, Vol. 7, Pages 438: The Properties of Meromorphic Multivalent q-Starlike Functions in the Janowski Domain

Fractal and Fractional doi: 10.3390/fractalfract7060438

Authors: Isra Al-Shbeil Jianhua Gong Samrat Ray Shahid Khan Nazar Khan Hala Alaqad

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.