Abstract
Let ℱ be a family of functions meromorphic in a domain D, let n ≥ 2 be a positive integer, and let a ≠ 0, b be two finite complex numbers. If, for each f ∈ ℱ, all of whose zeros have multiplicity at least k + 1, and f + a(f(k))n ≠ b in D, then ℱ is normal in D.
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