We consider the convolution of half-plane harmonic mappings with respective dilatations (z+
a)/(1+ az)(z+ a)/(1+ az) and e^ i θ z^ n ei θ zn, where-1< a< 1-1< a< 1 and θ ∈ R, n ∈ N θ∈ …

In this paper, we introduce a new class SH šk, g; fŽ of harmonic quasiconformal mappings,
where k A ½0, 1Ž, g A ½0, pŽ and f is an analytic function. Sufficient conditions for the linear …

In the present paper, we prove the convolutions of generalized harmonic right half-plane
mappings with harmonic vertical strip mappings are univalent and convex in the horizontal …

We first prove that the convolution of a normalized right half-plane mapping with another
subclass of normalized right half-plane mappings with the dilatation− z (a+ z)/(1+ az) is CHD …

The family Fλ of orientation-preserving harmonic functions f= h+ g in the unit disc D
(normalised in the standard way) satisfying h (z)+ g (z)= 1 (1+ λz)(1+ λz), z∈ D, for some …

We prove that convolutions of harmonic right half-plane mappings with harmonic vertical
strip mappings are univalent and convex in the horizontal direction. The proofs of these …

Due to the limitations of the harmonic convolution defined by Clunie and Sheil Small (Ann
Acad Sci Fenn Ser AI Math 9: 3–25, 1984), a new product⊗ has been recently introduced …

ON CONVOLUTIONS OF HARMONIC UNIVALENT MAPPINGS CONVEX IN THE DIRECTION
OF THE REAL AXIS 1. Introduction Page 1 Journal of Applied Analysis and Computation …

We consider classes of harmonic univalent functions fk= hk+ gk¯,(k= 1, 2) that are shears of
the analytic map hk− gk= 1/2 log⁡[1+ z/1− z] with dilatation ω k= ei θ kzk. We prove that if the …

In this article, we investigate meromorphic univalent harmonic functions having a simple
pole at the origin. First we establish sufficient conditions for the univalence of function f …