On value distribution of f^(k)-afⁿ

Abstract

The aim of this paper is to discuss the value distribution of the function f^(k) − afⁿ. Under the assumption that f(z) is a transcendental meromorphic function in the complex plane and a is a non-zero constant, it is proved that if n ⩽ k + 3, then f^(k) − afⁿ has infinitely many zeros. The main result is obtained by using the Nevanlinna theory and the Clunie lemma of complex functions.

Keywords

meromorphic function / zero point / value distribution / 30D30 / 30D35

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