Open Access
2014 Landau-Type Theorems for Certain Biharmonic Mappings
Ming-Sheng Liu, Zhen-Xing Liu, Jun-Feng Xu
Abstr. Appl. Anal. 2014(SI07): 1-7 (2014). DOI: 10.1155/2014/925947

Abstract

Let F ( z ) = | z | 2 g ( z ) + h ( z ) ( | z | < 1 ) be a biharmonic mapping of the unit disk 𝔻 , where g and h are harmonic in 𝔻 . In this paper, the Landau-type theorems for biharmonic mappings of the form L ( F ) are provided. Here L represents the linear complex operator L = (z / z) - (z ¯ / z) ¯ defined on the class of complex-valued C 1 functions in the plane. The results, presented in this paper, improve the related results of earlier authors.

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Ming-Sheng Liu. Zhen-Xing Liu. Jun-Feng Xu. "Landau-Type Theorems for Certain Biharmonic Mappings." Abstr. Appl. Anal. 2014 (SI07) 1 - 7, 2014. https://doi.org/10.1155/2014/925947

Information

Published: 2014
First available in Project Euclid: 6 October 2014

MathSciNet: MR3191077
zbMATH: 1291.30127
Digital Object Identifier: 10.1155/2014/925947

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI07 • 2014
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