## Abstract and Applied Analysis

### Landau-Type Theorems for Certain Biharmonic Mappings

#### Abstract

Let $F(z)=|z{|}^{2}g(z)+h(z) (|z|<1)$ be a biharmonic mapping of the unit disk $\mathrm{\Bbb D}$, where $g$ and $h$ are harmonic in $\mathrm{\Bbb D}$. In this paper, the Landau-type theorems for biharmonic mappings of the form $L(F)$ are provided. Here $L$ represents the linear complex operator $L=\mathrm{(z}\partial /\partial \mathrm{z)}-\overline{\mathrm{(z}}\partial /\partial \overline{\mathrm{z)}}$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 925947, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412605993

Digital Object Identifier
doi:10.1155/2014/925947

Mathematical Reviews number (MathSciNet)
MR3191077

Zentralblatt MATH identifier
1291.30127

#### Citation

Liu, Ming-Sheng; Liu, Zhen-Xing; Xu, Jun-Feng. Landau-Type Theorems for Certain Biharmonic Mappings. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 925947, 7 pages. doi:10.1155/2014/925947. https://projecteuclid.org/euclid.aaa/1412605993

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