[PDF] Top 20 Uniqueness of entire functions sharing two values with their difference operators

... Let f (z) and g(z) be two nonconstant meromorphic functions, and let a be an arbitrary complex constant. If f (z) – a and g(z) – a have the same zeros counting multiplicities (ig- noring multiplicities), we ... See full document

... their difference operators (see, ...the uniqueness problems on the case that shifts or differ- ence polynomials of two entire functions share a small ...the uniqueness ... See full document

... Meromorphic functions is an important part of Nevan- linna ...difference operators. Then many authors started to investigate the uniqueness of meromorphic functions sharing ... See full document

... of sharing small ...nonconstant entire function; let a ≡ 0 be a small function related to f ; and let k ≥ 2 be a positive ...meromorphic functions with respect to differ- ence has become a subject of ... See full document

... The difference Nevanlinna theory and its applications to the uniqueness theory have become a subject of great interest [2-4], ...(z) sharing values with its shift f(z + c), we recall a key ... See full document

... Throughout this paper, a meromorphic function always means meromorphic in the whole complex plane, and c always means a nonzero constant. We use the basic notations of the Nevanlinna theory of meromorphic ... See full document

... shifts and proved some original results corresponding to Nevanlinna’s five-value theorem and four-value theorem; Chen and Yi [3], Li and Gao [14], and Liu and Yang [16] studied uniqueness of entire ... See full document

... meromorphic functions of finite order and their difference operators are identical, if they share four small functions “IM”, or share two small functions and ∞ ...small functions, ... See full document

... a uniqueness result of entire functions that share a small entire function with their two difference operators, generalizing some previous theorems of (Farissi et ...small ... See full document

... Certain estimates involving the derivative f 7→ f 0 of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory. Recently, there has been an increasing interest in ... See full document

... of difference operators of meromorphic functions (see ...the uniqueness results of difference polynomials of meromorphic functions, their shifts and difference ... See full document

... Currently, there has been an increasing interest in studying difference equations in the complex plane. Halburd and Korhonen [4,5] established a version of Nevanlinna theory based on difference ... See full document

... obtained in the paper significantly improve a number of existing results. Further, using the notion of weighted sharing of sets, we deal the same problem. We exhibit a handful number of examples to justify certain ... See full document

... difference operators; see, ...the uniqueness of meromorphic functions sharing values or small functions with their shifts (see, ...difference operators (see, ... See full document

... an entire function is equal to its difference operator if it has a growth property and shares a set, where the set consists of two entire functions of smaller ... See full document

... Definition 5 Let a, f be two meromorphic functions. If T (r, a) = S(r, f ), where S(r, f ) = o(T (r, f )), as r → ∞ outside of a possible exceptional set of finite logarithmic measure. Then we say that a is a ... See full document

... of functions f and g in F , f (k) and g (k) share p(z) in D, then F is normal in ...meromorphic functions in D; the multiplicity of all zeros and poles of f ∈ F is at least k + ...of functions f and ... See full document

... Let f (z) and g(z) be two nonconstant meromorphic functions for some a ∈ C ∪ {∞}. If the zeros of f (z) – a and g(z) – a (if a = ∞ , zeros of f (z) – a and g(z) – a are the poles of f (z) and g(z) ... See full document

... A meromorphic function f (z) means meromorphic in the complex plane C . If no poles occur, then f (z) reduces to an entire function. For every real number x ≥ , we define log + x := max {, log x}. Assume that ... See full document

... For two meromorphic functions defined in C, there are many uniqueness theorems when they share small functions az is called a small function of fz if T r, az oT r, f r → ∞ see ...small ... See full document