Convex null sequence technique for analytic and univalent mappings of the unit disk

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.

Convex and Starlike Univalent Functions

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.

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...

Coefficient estimates for a subclass of analytic and bi-univalent functions

In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk. Upper bounds for the second and third coefficients of functions in this subclass are founded. Our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.