A new class of harmonic functions associated with A (p,q)-Ruscheweyh operator

Abstract

With the use of post-quantum or (p; q)-calculus, in this paper, we define a new class S⁰_H (n; p; q; α) of certain harmonic functions f ∈ 2 S⁰_H associated with a (p; q)-Ruscheweyh operator Rⁿ_p,q: For functions in this class, we obtain a necessary and sufficient convolution condition. A sufficient coefficient inequality is given for functions f ∈ 2 S⁰_H (n; p; q; α). It is proved that this coefficient inequality is necessary for functions in its subclass TS⁰_H (n; p; q; α): Certain properties such as convexity, compactness, and results on bounds, extreme points are also derived for functions in the subclass TS⁰_H (n; p; q; α).