Partial Sums of Generalized Harmonic Starlike Univalent Functions Generated by a (p,q)-Ruscheweyh-Type Harmonic Differential Operator

Abstract

Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f (0) = fz (0) 1 = 0. In this paper, we define a new generalized subclass of H associated with the (p, q) Ruscheweyh-type harmonic differential operator in D. We first obtain a sufficient coefficient condition that guarantees that a function f in H is sense-preserving harmonic univalent in D and belongs to the aforementioned class. Using this coefficient condition, we then examine ratios of partial sums of f in H. In all cases the results are sharp. In addition, the results so obtained generalize the related works of some authors, and many other new results are obtained.