Partial sums of generalized harmonic starlike univalent functions generated by a (p,q)–Ruscheweyh-type harmonic differential operator

Let ℌ denote the class of complex-valued harmonic functions f defined in the open unit disc \(\mathbb{D}\) $$\mathbb{D}$$ and normalized by f(0) = f_z(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 \(\mathbb{D}\) $$\mathbb{D}$$ . We first obtain a sufficient coefficient condition that guarantees that a function f in ℌ is sense-preserving harmonic univalent in \(\mathbb{D}\) $$\mathbb{D}$$ 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.