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...

A continuous complex-valued function f u iv is said to be harmonic in a simply connected domain D if both u and v are real harmonic in D. In any simply-connected domain we can write f h g, where 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 sense-preserving in D is that |h′ z | > |g...

The aim of the present paper is to study a certain subclass of harmonic univalent functions with varying arguments defined by Salegean operator. For this class we determine a sufficient coefficient condition, representation theorem, distortion theorem, extreme points. Mathematics Subject Classification: Primary 30C45; Secondary 30C80

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.