Certain New Class of Harmonic Functions Involving Quantum Calculus. (25th May 2022) - Khan, Mohammad Faisal
Abstract : 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 ∈ H 0 . We investigate a new class S H 0 m, q, α of harmonic functions f ∈ H 0 . In this class, we prove a necessary and sufficient convolution condition for the functions f ∈ H 0 and also we proved that this sufficient coefficient condition is sense preserving and univalent in the class S H 0 m, q, α . It is proved that this coefficient condition is necessary for the functions in its subclass T S H 0 m, 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 T S H 0 m, q, α . Also we obtained extreme points for the functions in the class T S H 0 m, q, α .