where h and g are analytic in D. We call h the analytic part and g the coanalytic part of f . A necessary and sufficient condition for f to be locally univalent and sense preserving in D is that |h z | > |g z | for all z in D see 1 . Let H be the class of functions of the form 1.1 that are harmonic univalent and sense preserving in the unit disk U {z : |z| < 1} for which f 0 fz 0 − 1 0. Then fo...

A comprehensive class of complex-valued harmonic prestarlike univalent functions is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Distortion bounds and extreme points are also obtained. 2000 Mathematics Subject Classification:Primary 30C45, 30C50.

f = u + iv is a complex harmonic function in a domain D if both u and v are real continuous harmonic functions in D. In any simply connected domain D ⊂ C, f is written in the form of f = h+g, where both h and g are analytic in D. We call h the analytic part and g the co-analytic part of f . A necessary and sufficient condition for f to be locally univalent and orientation preserving in D is tha...

The first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right halfplane mapping or a normalized vertical strip mapping is convex in the direction of the real axis. provided that it is locally univalent. In this paper, we prove that in general the assumption of local univalency cannot be omitted. However, we are able to show t...

The purpose of this work is to present a class harmonic univalent functions de?ned by the Dziok-Srivastava operator. Some geometric properties like coefficients conditions, distortion theorem, convolution (Hadamard product), convex combination and extreme points are investigated.&#x0D; 2000 Mathematics Subject Classi?cation: 30C45, 30C50