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On the Nevanlinna’s theory for vector-valued mappings. (English) Zbl 1194.30035
Summary: The purpose of this paper is to establish the first and second fundamental theorems for $E$-valued meromorphic mappings from a generic domain $D\subset \Bbb C$ to an infinite dimensional complex Banach space $E$ with a Schauder basis. This is a continuation of the work of {\it C.-G. Hu} and {\it Q. Hu} [Complex Var. Elliptic Equ. 51, No. 8--11, 777--791 (2006; Zbl 1183.30027)]. For $f(z)$ defined in the disk, we will prove Chuang’s inequality, which compares the relationship between $T(r,f)$ and $T(r,f^{\prime})$. Consequently, we obtain that the order and the lower order of $f(z)$ and its derivative $f^{\prime}(z)$ are the same.

MSC:
 30D35 Distribution of values (one complex variable); Nevanlinna theory
Full Text:
References:
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