Abstract and Applied Analysis

Landau-Type Theorems for Certain Biharmonic Mappings

Ming-Sheng Liu, Zhen-Xing Liu, and Jun-Feng Xu

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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.

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

Permanent link to this document
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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