Certain New Class of Harmonic Functions Involving Quantum Calculus - Mohammad Faisal Khan (Journal of Function Spaces)
Here in this paper, we are using the concepts of q-calculus operator theory associated with harmonic functions and define the q-Noor integral operator for harmonic functions f∈H0. We investigate a new class SH0m,q,α of harmonic functions f∈H0. In this class, we prove a necessary and sufficient convolution condition for the functions f∈H0 and also we proved that this sufficient coefficient condition is sense preserving and univalent in the class SH0m,q,α. It is proved that this coefficient condition is necessary for the functions in its subclass TSH0m,q,α. By using this necessary and sufficient coefficient condition, we obtained results based on the convexity and compactness and results on the radii of q-starlikeness and q-convexity of order α in the class TSH0m,q,α. Also we obtained extreme points for the functions in the class TSH0m,q,α.