On the Nevanlinna's theory for vector-valued mappings (Q981112)

Summary: The purpose of this paper is to establish the first and second fundamental theorems for \(E\)-valued meromorphic mappings from a generic domain \(D\subset \mathbb C\) to an infinite dimensional complex Banach space \(E\) with a Schauder basis. This is a continuation of the work of \textit{C.-G. Hu} and \textit{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.