On the Zeros of the Differential Polynomials φfl(f(k))n−a

Abstract

Letting f be a transcendental meromorphic function, we consider the value distribution of the differential polynomials φfl(f(k))n−a, where φ(≢0) is a small function of f, l(≥2), n(≥1), k(≥1) are integers and a is a non-zero constant, and obtain an important inequality concerning the reduced counting function of φfl(f(k))n−a. Our results improve and generalize the results obtained by Xu and Ye, Karmakar and Sahoo, Chakraborty et.al, and Chen and Huang.