Meromorphic Function that Shares One Small Function with its Differential Polynomial

Abstract

In this paper, we investigate the uniqueness problems of meromorphic functions that share a small function with its differential polynomials, and give a result which is related to a conjecture of R. Brück and improve the results of I. Lahiri and Q. C. Zhang.

A Further Result Related to a Conjecture of R. Brück

“…In 1999, Yang [10] confirmed that the Conjecture is also true when f is replaced by f (k) (k ≥ 2) and f is of finite order. In recent years, many results have been published concerning the above conjecture, see [2,5,7,8,14,15,16,17,18] etc., and Zhang [17] was the first author who considers the case when f is a meromorphic function. We need the following definition.…”

On the Value Distribution of Differential Polynomials

“…Since q 0j ≥ 1, it is clear from equation (4) Proof. The proof is similar to the proof of the Lemma 2.4 of ( [6]).…”

On the Generalizations of Brück Conjecture

“…As (f (k) ) m is simply a special differential monomial in f , it will be interesting to investigate whether Theorems D-H can be extended up to differential polynomial generated by f . In this direction recently Li and Yang [11] improved Theorem D in the following manner.…”