Abstract
In this paper, we study the zero distributions on the derivatives of q-shift dif- ference polynomials of meromorphic functions with zero order and obtain two theorems that extend results of (3).
Highlights
In this paper, a meromorphic functions f means meromorphic in the complex plane
Throughout of this paper, we denote by ρ(f ) and ρ2(f ) the order of f and the hyper order of f (Laine, 1993 and Yang and Yi, 2003)
We assume that the reader is familiar with standard symbols and fundamental results of Nevanlinna Theory(Halburd Korhonen and Tohge; Laine, 1993 and Yang and Yi, 2003)
Summary
A meromorphic functions f means meromorphic in the complex plane. If no poles occur, f reduces to an entire function. (Liu, Liu and Coa, 2012) Let f be a transcendental meromorphic function of ρ2(f ) < 1. (Liu, Liu and Coa, 2012) Let f and g be a transcendental entire function of ρ2(f ) < 1, n ≥ 2k + m + 6. (Harina P.W and Tanuja A, 2013) Let f and g be a transcendental meromorphic function with zero order. If n ≥ 10k + 14(n ≥ 5k + 12), [P (f )f (qz + c)](k) and [P (g)g(qz + c)](k) share the 1 IM, the conclusion of theorem 1 still holds
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