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.