Abstract and Applied Analysis
Volume 2010 (2010), Article ID 864539, 15 pages
doi:10.1155/2010/864539
Research Article

On the Nevanlinna's Theory for Vector-Valued Mappings

Zu-Xing Xuan1,2 and Nan Wu1

1Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
2Basic Department, Beijing Union University, No.97, Bei Si Huan Dong Road, Chaoyang District, Beijing 100101, China

Received 7 September 2009; Revised 25 January 2010; Accepted 17 April 2010

Academic Editor: Jean Pierre Gossez

Copyright © 2010 Zu-Xing Xuan and Nan Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this paper is to establish the first and second fundamental theorems for an E-valued meromorphic mapping from a generic domain D⊂ℂ to an infinite dimensional complex Banach space E with a Schauder basis. It is a continuation of the work of C. Hu and Q. Hu. For f(z) defined in the disk, we will prove Chuang's inequality, which is to compare the relationship between T(r,f) and T(r,f′). Consequently, we obtain that the order and the lower order of f(z) and its derivative f′(z) are the same.