TY - JOUR

T1 - Applications of a q-Differential Operator to a Class of Harmonic Mappings Defined by q-Mittag–Leffler Functions

AU - Khan, Mohammad Faisal

AU - Al-shbeil, Isra

AU - Khan, Shahid

AU - Khan, Nazar

AU - Haq, Wasim Ul

AU - Gong, Jianhua

N1 - Funding Information:
This research was funded by UPAR 31S315, United Arab Emirates University.
Publisher Copyright:
© 2022 by the authors.

PY - 2022/9

Y1 - 2022/9

N2 - 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 (Formula presented.) -variations.

AB - 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 (Formula presented.) -variations.

KW - harmonic functions

KW - Janowski function

KW - q-derivative operator

KW - q-Mittag–Leffler functions

KW - quantum (or q-)calculus

KW - starlike functions

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U2 - 10.3390/sym14091905

DO - 10.3390/sym14091905

M3 - Article

AN - SCOPUS:85138512566

VL - 14

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 9

M1 - 1905

ER -