Planar harmonic functions are complex-valued functions whose real and imaginary parts are
not necessarily conjugate, ie, do not need to satisfy the Cauchy-Riemann equations …

Let HH denote the class of harmonic functions f defined in D:={z ∈ C:| z|< 1\} D:= z∈ C:| z|<
1, and normalized by f (0)= 0= f_ z (0)-1 f (0)= 0= fz (0)-1. In this paper, for α ≥ 0 α≥ 0, we …

In this paper, we establish a coefficient bound for quasiregular and elliptic harmonic
mappings and using these bounds, we establish Landau-Bloch type theorem for (K, K′) …

For, let denote the class of sense preserving harmonic mappings in the unit disk satisfying.
The main aim of this paper is to study some basic properties such as coefficient bounds …

In this paper, we first establish the sharp version of Landau–Bloch type theorem for strongly
bounded harmonic mappings by considering the Landau–Bloch type theorem of a one …

Full article: Bloch-type theorems for meromorphic harmonic mappings Skip to Main Content
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In this paper, we obtain growth, covering, and area theorems for certain families of sense
preserving univalent harmonic functions which are close-to-convex in the unit disk D D. We …

Let G_H^ k (α; r) GH k (α; r) denote the subclasses of normalized harmonic mappings f= h+
̄ gf= h+ g¯ in the unit disk D satisfying the condition Re\,((1-α) h (z) z+ α h'(z))>|(1-α) g (z) z+ …

We introduce a new subclass of close-to-convex harmonic mappings in the unit disk, which
originates from the work of P. Mocanu on univalent mappings. We also give coefficient …

Abstract Let P0 H (M) denote the class of normalised harmonic mappings f= h+ g in the unit
disk D satisfying Re (zh (z))>− M+| zg (z)|, where h (0)− 1= 0= g (0) and M> 0. Let B0 H (M) …