# ON UNIVALENT HARMONIC FUNCTIONS

@inproceedings{ztrk2002ONUH, title={ON UNIVALENT HARMONIC FUNCTIONS}, author={M. {\"O}zt{\"u}rk and S. Yalçın}, year={2002} }

Two classes of univalent harmonic functions on unit disc satisfying the conditions P 1 are given. That the ranges of the functions belonging to these two classes are starlike and convex, respectively. Sharp coefficient relations and distortion theorems are given for these functions. Furthermore results concerning the convolutions of functions satisfying above inequalities with univalent, harmonic and convex functions in the unit disk and with harmonic functions having positive real part.

#### 51 Citations

ON A SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS

- 2008

The class of univalent harmonic functions on the unit disc satisfying the condition ∑∞ k=2 (k m − αk)(|ak|+ |bk|) ≤ (1−α)(1−|b1|) is given. Sharp coefficient relations and distortion theorems are… Expand

ON A SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS

- Mathematics
- 2018

Convex harmonic functions, Starlike harmonic functions, extremal problems. Abstract: The class of univalent harmonic functions on the unit disc satisfying the condition P 1 k=2 (k m k n )(|a k|+|bk|)… Expand

On a certain class of harmonic multivalent functions.

- Mathematics
- 2011

The purpose of the present paper is to study some results in- volving coe-cient conditions, extreme points, distortion bounds, convolution conditions and convex combination for a new class of… Expand

ON MULTIVALENT HARMONIC MEROMORPHIC FUNCTIONS INVOLVING HYPERGEOMETRIC FUNCTIONS

- Mathematics
- 2011

paper we introduce a subclass of multivalent harmonic meromorphic functions defined in the exterior of the unit disk by using generalize hypergeometric functions. We derived sufficient coefficient… Expand

Polynomial approximation of harmonic mappings

- Mathematics
- 2013

This study is concerned with univalent harmonic mappings on the unit disc of the complex plane. We examine a family of harmonic polynomials that have some interesting geometric properties, e.g. the… Expand

Subordination results on harmonic k-uniformly convex mappings and related classes

- Computer Science, Mathematics
- Comput. Math. Appl.
- 2010

Some connections between certain classes of harmonic univalent functions are established by applying a number of convolution properties involving hypergeometric functions by investigating such connections with harmonic k-uniformly convex and a related class k-ST mappings in the plane. Expand

A new class of harmonic univalent functions by the generalized Salagean operator

- Wuhan University Journal of Natural Sciences
- 2007

AbstractA complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form
$$f = h + \bar g$$
, where h and g are analytic in U. We define and… Expand

A Subclass of Harmonic Univalent Functions Associated with -Analogue of Dziok-Srivastava Operator

- Mathematics
- 2013

We study a class of complex-valued harmonic univalent
functions using a generalized operator involving basic hypergeometric
function. Precisely, we give a necessary and sufficient coefficient… Expand

On Certain Class of Meromorphic Harmonic Concave Functions

- Mathematics
- 2015

In this paper, a class of meromorphic harmonic functions concave in the unit disc is introduced. Coefficient bounds, distortion inequalities, extreme points, geometric convolution, integral… Expand

Estimates of integral means of harmonic mappings

- Mathematics
- 2000

In this paper we prove that each univalent harmonic mapping of the unit disc onto a given horizontal strip is in h 1 and we find a uniform upper bound for their h 1-norm. We also give some estimates… Expand

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