Abstract
Let f be a transcendental meromorphic function and n, k be two positive integers. Then af(f (k))n − 1, n >- 2, has infinitely many zeros, where a(z) ≢ 0 is a meromorphic function such that T(r, a) = S(r, f).
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References
W. Bergweiler and A. Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana, 11 1995) 2, 355–373.
W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math. (2) 70 (1959), 9–42.
W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs. Clarendon Press, Oxford, 1964.
W. K. Hayman and J. Miles, On the growth of a meromorphic function and its derivatives, Complex Variables Theory Appl. 12 1989) 1-4, 245–260.
Y. F. Wang, C. C. Yang and L. Yang, On the zeros of f(f (k))n − a, Kexue Tongbao 38 (1993), 2215–2
Zhong Fa Zhang and Guo Dong Song, On the zeros of f(f (k))n − a(z), Chinese Ann. Math. Ser. A 19 1998) 2, 275–
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Alotaibi, A. On the Zeros of af(f (k))n − 1 for n ≥ 2. Comput. Methods Funct. Theory 4, 227–235 (2004). https://doi.org/10.1007/BF03321066
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DOI: https://doi.org/10.1007/BF03321066