Let f be a sense-preserving harmonic mapping in the unit disk. We give a sufficient condition in terms of the pre-Schwarzian derivative of f to ensure that it can be extended to a quasiconformal map in the complex plane. Introduction A well-known criterion due to Becker [5] states that if a locally univalent analytic function φ in the unit disk D satisfies (1) sup z∈D ∣∣∣∣φ′′(z) φ′(z) ∣∣∣∣ (1− ...

A recent result of Yalcin [9] appeared in Applied Mathematics Letters (2005), concerning the convolution of two harmonic univalent functions in class SH(m,n, α) is improved. AMS (MOS) Subject Classification Codes: 30C45

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.

In the present paper, we consider a generalised subclass of analytic functions involving arithmetic, geometric and harmonic means. For this function class we obtain an inclusion result, Fekete-Szegö inequality and coefficient bounds for bi-univalent functions.

This paper aims to introduce a measure of the non-univalency harmonic mapping. By using it, we find best approximation an analytic function by univalent