Summary.
We show that each transcendental meromorphic solution f(z) of the functional equation \( \sum_{j=0}^na_j(z)f(c^jz) = Q(z) \), where Q and the \( a_{j},\,j = 0, \dots, n \) are polynomials without common zeros, \( a_n(z)a_0(z) \ne 0 \) and 0 < |c| < 1, satisfies \( m(r,f) = \sigma_f(\log r)^2(1+o(1)) \) for some constant \( \sigma_f \).
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Received: April 3, 2000, revised version: July 31, 2000.
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Bergweiler, W., Ishizaki, K. & Yanagihara, N. Growth of meromorphic solutions of some functional equations I. Aequat. Math. 63, 140–151 (2002). https://doi.org/10.1007/s00010-002-8012-x
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DOI: https://doi.org/10.1007/s00010-002-8012-x