Paper Info
Title
Applications of a q-Differential Operator to a Class of Harmonic Mappings Defined by q-Mittag-Leffler Functions
Abstract
Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of differential operators for harmonic functions with the help of basic concepts of quantum (q-) calculus operator theory; and introduce a new subclass of harmonic functions associated with the Janowski and q-Mittag-Leffler functions. We obtain several useful properties of the new class, such as necessary and sufficient conditions, criteria for analyticity, compactness, convexity, extreme points, radii of starlikeness, radii of convexity, distortion bounds, and integral mean inequality. Furthermore, we discuss some applications of this study in the form of some results and examples and highlight some known corollaries for verifying our main results presented in this investigation. Finally, the conclusion section summarizes the fact about the (p, q)-variations.
Year
DOI
Venue
2022
10.3390/sym14091905
SYMMETRY-BASEL
Keywords
DocType
Volume
quantum (or q-)calculus, q-derivative operator, harmonic functions, Janowski function, starlike functions, q-Mittag-Leffler functions
Journal
14
Issue
ISSN
Citations 
9
2073-8994
0
PageRank 
References 
Authors
0.34
0
6
Name
Order
Citations
PageRank
Mohammad Faisal Khan100.68
Isra Al-shbeil200.34
Shahid Khan301.01
Nazar Khan4156.38
Wasim Ul Haq500.34
Jianhua Gong600.68