We prove several improved versions of Bohr's inequality for the harmonic map**s of the
form f= h+ g¯, where h is bounded by 1 and| g′(z)|≤| h′(z)|. The improvements are …

Let F denote the class of all normalized analytic functions f that are locally univalent in the
unit disk| z|< 1 satisfying the condition Re (1+ zf ″(z) f′(z))>− 1 2 for| z|< 1. Functions in F …

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 derive several sufficient conditions of the linear combinations of harmonic
univalent map**s to be univalent and convex in the direction of the real axis. Furthermore …

Let HC (ϕ) and HC c (ϕ) denote the classes of sense-preserving harmonic map**s f= h+
g¯ in D with the dilation g′(z)= α zh′(z) for| α|< 1 such that h is Ma–Minda type convex …

Planar harmonic map**s underly the theory of minimal surfaces in three space. The
seminal paper [13] introduced a complex analytic approach for their studies. Ever since this …

Planar harmonic univalent map**s have long been used in the representation of minimal
surfaces. Such map**s and related functions have applications in the seemingly diverse …

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

Lawrence Zalcman's conjecture states that if f (z)= z+ ∑ n= 2^ ∞ a_ nz^ nf (z)= z+∑ n= 2∞
anzn is analytic and univalent in the unit disk| z|< 1| z|< 1, then| a_n^ 2-a_ 2n-1| ≦ (n-1)^ 2 …