Generalized q-starlike harmonic functions (vol 115, 176, 2021)

In this paper a class SH0(n,q,A,B) of harmonic functions f∈ H, associated with a q-Ruscheweyh operator is defined. A necessary and sufficient convolution condition for a function f∈ H to be in this class is proved. A sufficient coefficient condition for the harmonic functions to be in SH0(n,q,A,B) and to be sense preserving and univalent is also obtained. It is proved that this coefficient condition is also necessary for the functions in its subclass TSH0(n,q,A,B). Using this necessary and sufficient coefficient condition, results based on the convexity and compactness of the class TSH0(n,q,A,B), extreme points for the functions in the class TSH0(n,q,A,B) are obtained. Further results on the radii of q -starlikeness of order α, for the functions in the class TSH0(n,q,A,B) are obtained. © 2021, The Royal Academy of Sciences, Madrid.