Abstract
We extend two theorems on fixpoints of f(z) by Langley and Zheng [1] to the consideration of points where f(z) = Q(z) for some rational function Q such that Q(∞) = ∞. In addition, we extend the class of functions f from transcendental entire functions to meromorphic functions with relatively few poles.
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J. K. Langley and J. H. Zheng. On the fixpoints, multipliers and value distribution of certain classes of meromorphic functions. Ann. Acad. Sci. Fenn. Math., 23(l):133–150, 1998.
W. Bergweiler. On the zeros of certain homogeneous differential polynomials. Arch. Math. (Basel), 64(3):199–202, 1995.
A. É. Erëmenko and M. Yu. Lyubich. Dynamical properties of some classes of entire functions. Ann. Inst. Fourier (Grenoble), 42(4):989–1020, 1992.
Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. (N.S.), 29(2):151–188, 1993.
P. Rippon and G. Stallard. Iteration of a class of hyperbolic meromorphic functions. Proc. Amer. Math. Soc., 127:3251–3258, 1999.
Sakari Toppila and Jörg Winkler. Some lower bounds for the maximal growth of the spherical derivative. Complex Variables Theory Appl, 2(l):l–25, 1983.
Ch. Pommerenke. Boundary behaviour of conformai mops, volume 299 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1992.
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Clifford, E.F. Extending Two Fixpoint Theorems of Langley and Zheng. Results. Math. 47, 45–54 (2005). https://doi.org/10.1007/BF03323011
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DOI: https://doi.org/10.1007/BF03323011