Uniqueness Problems about Entire Functions with Their Difference Operator Sharing Sets

Entire functions sharing a small entire function‎ ‎with their difference operators

In this paper, we mainly investigate the uniqueness of the entire function sharing a small entire function with its high difference operators. We obtain one results, which can give a negative answer to an uniqueness question relate to the Bruck conjecture dealt by Liu and Yang. Meanwhile, we also establish a difference analogue of the Bruck conjecture for entire functions of order less than 2, ...

Uniqueness Theorems of Difference Operator on Entire Functions

A function f(z) is called meromorphic, if it is analytic in the complex plane except at poles. It is assumed that the reader is familiar with the standard symbols and fundamental results of Nevanlinna theory such as the characteristic function T(r, f), and proximity function m(r, f), counting function N(r, f) (see [1, 2]). In addition we use S(r, f) denotes any quantity that satisfies the condi...

Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives

and Applied Analysis 3 From the ideas of Theorem D to Theorem F, it is natural to ask whether the values a, b in Theorem C can be replaced by two polynomials Q1, Q2. The main purpose of this paper is to investigate this problem. We prove the following result. Theorem 1.2. Let Q1 z a1z a1,p−1zp−1 · · · a1,0 and Q2 z a2z a2,p−1zp−1 · · · a2,0 be two polynomials such that degQ1 z degQ2 z p (where ...

Uniqueness of entire functions sharing two values with their difference operators

entire functions sharing a small entire function‎ ‎with their difference operators

in this paper, we mainly investigate the uniqueness of the entire function sharing a small entire function with its high difference operators. we obtain one results, which can give a negative answer to an uniqueness question relate to the bruck conjecture dealt by liu and yang. meanwhile, we also establish a difference analogue of the bruck conjecture for entire functions of order less than 2, ...