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- Title
Applications of Symmetric Quantum Calculus to the Class of Harmonic Functions.
- Authors
Khan, Mohammad Faisal; Al-Shbeil, Isra; Aloraini, Najla; Khan, Nazar; Khan, Shahid
- Abstract
In the past few years, many scholars gave much attention to the use of q-calculus in geometric functions theory, and they defined new subclasses of analytic and harmonic functions. While using the symmetric q-calculus in geometric function theory, very little work has been published so far. In this research, with the help of fundamental concepts of symmetric q-calculus and the symmetric q-Salagean differential operator for harmonic functions, we define a new class of harmonic functions connected with Janowski functions S H 0 ˜ m , q , A , B . First, we illustrate the necessary and sufficient convolution condition for S H 0 ˜ m , q , A , B and then prove that this sufficient condition is a sense preserving and univalent, and it is necessary for its subclass TS H 0 ˜ m , q , A , B . Furthermore, by using this necessary and sufficient coefficient condition, we establish some novel results, particularly convexity, compactness, radii of q-starlike and q-convex functions of order α , and extreme points for this newly defined class of harmonic functions. Our results are the generalizations of some previous known results.
- Subjects
HARMONIC functions; STAR-like functions; GEOMETRIC function theory; UNIVALENT functions; CALCULUS; ANALYTIC functions; DIFFERENTIAL operators
- Publication
Symmetry (20738994), 2022, Vol 14, Issue 10, pN.PAG
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym14102188