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Fixed points of meromorphic functions and of their differences and shifts

Tom 109 / 2013

Zong-Xuan Chen Annales Polonici Mathematici 109 (2013), 153-163 MSC: Primary 30D35; Secondary 39A10. DOI: 10.4064/ap109-2-4

Streszczenie

Let $f(z)$ be a finite order transcendental meromorphic function such that $\lambda (1/f(z))<\sigma (f(z))$, and let $c\in \mathbb {C}\setminus \{0\}$ be a constant such that $f(z+c)\not \equiv f(z)+c$. We mainly prove that $$\eqalign {\max\{\tau (f(z)), \tau (\Delta _c f(z))\}&=\max\{\tau (f(z)), \tau (f(z+c))\} \cr &=\max\{\tau (\Delta _c f(z)), \tau (f(z+c))\}=\sigma (f(z)), }$$where $\tau (g(z))$ denotes the exponent of convergence of fixed points of the meromorphic function $g(z)$, and $\sigma (g(z))$ denotes the order of growth of $g(z).$

Autorzy

  • Zong-Xuan ChenSchool of Mathematical Sciences
    South China Normal University
    510631, Guangzhou, P.R. China
    e-mail

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