## 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.

Original language | English |
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Article number | 438 |

Journal | Fractal and Fractional |

Volume | 7 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 2023 |

## Keywords

- Janowski functions
- Sălăgean q-differential operator
- meromorphic multivalent q-starlike functions
- q-derivative operator
- quantum (or q-) calculus

## ASJC Scopus subject areas

- Analysis
- Statistical and Nonlinear Physics
- Statistics and Probability