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On the Nevanlinna′s Theory for Vector‐Valued Mappings

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  • Zu-Xing Xuan
  • Nan Wu

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.

Suggested Citation

  • Zu-Xing Xuan & Nan Wu, 2010. "On the Nevanlinna′s Theory for Vector‐Valued Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:864539
    DOI: 10.1155/2010/864539
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    References listed on IDEAS

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    1. Jianhua Zheng, 2010. "Meromorphic Functions with Radially Distributed Values," Springer Books, in: Value Distribution of Meromorphic Functions, chapter 0, pages 207-228, Springer.
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    Cited by:

    1. Zhaojun Wu & Zuxing Xuan, 2012. "Characteristic Functions and Borel Exceptional Values of E‐Valued Meromorphic Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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