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On the fix-points of composite meromorphic functions and generalizations

Authors Yang, Chung-Chun HKUST affiliated (currently or previously)
Zheng, Jian-Hua
Issue Date 1996
Source Journal d Analyse Mathematique , v. 68, 1996, p. 59-93
Summary Let us begin with introducing the following fundamental notations and definition. Let f(z) be a transcendental function meromorphic in the complex plane. Throughout this paper, we denote by p(f), λ(f) and σ(f) the order, lower order of f(z), and exponent of convergence for its zeros, respectively and by E and F sets on the positive real axis with, respectively, finite linear measure and finite logarithmic measure, not necessarily the same at each occurrence. And we denote by S(r,f) a quantity S(r,f) = o(T(r,f)), as r → ∞, possible outside a set of finite linear measure. We say that a meromorphic function γ(z) is a small meromorphic function with respect to f(z), provided that T(r,γ) = S(r,f). Let g(z) be a transcendental entire function, or else meromorphic if f(z) is a rational function.
ISSN 0021-7670
Rights © 1996 The Magnes Press, The Hebrew University, Jerusalem. Reproduced with permission.
Language English
Format Article
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