A Class of Univalent Biharmonic Mappings

On Univalent Solutions of the Biharmonic Equation

Planar Harmonic Univalent and Related Mappings

The theory of harmonic univalent mappings has become a very popular research topic in recent years. The aim of this expository article is to present a guided tour of the planar harmonic univalent and related mappings with emphasis on recent results and open problems and, in particular, to look at the harmonic analogues of the theory of analytic univalent functions in the unit disc.

Univalent Harmonic Mappings Convex in One Direction

In this work some distortion theorems and relations between the coefficients of normalized univalent harmonic mappings from the unit disc onto domains on the direction of imaginary axis are obtained.

Harmonic Univalent Mappings and Linearly Connected Domains

We investigate the relationship between the univalence of f and of h in the decomposition f = h+g of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + g with |g| < c|h| is univalent. The notion of a linearly connected domain appea...

On a Class of Univalent Functions

We consider the class of univalent functions f(z)= z+a3z3+a4z4+··· analytic in the unit disc and satisfying |(z2f ′(z)/f 2(z))−1|< 1, and show that such functions are starlike if they satisfy |(z2f ′(z)/f 2(z))−1|< (1/√2).