This article is cited in 2 papers

The Schwarzian derivatives of harmonic functions and univalence conditions

S. Yu. Graf<sup>ab

a</sup> Tver State University, 33, Zheliabova st., Tver 170100, Russia
^b Petrozavodsk State University, 33, Lenina st., Petrozavodsk 185910, Russia

Abstract: In the paper we obtain some analogues of Nehari's univalence conditions for sense-preserving functions that are harmonic in the unit disc $\Bbb D=\{z\in\Bbb C:\,|z|<1\}$.

Keywords: harmonic mappings, univalence criteria, Schwarzian derivative.

UDC: 517.54

MSC: 30C45, 30C55, 30C99

Received: 13.09.2017
Revised: 08.12.2017
Accepted: 13.12.2017

Language: English

DOI: 10.15393/j3.art.2017.4230

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