[PDF] Top 20 Uniqueness of Meromorphic Functions with Their Nonlinear Differential Polynomials Share a Small Function

... poles of f(z) with multiplicities  k , and by N k )  r f ,  the corresponding one for which the multiplicity is not counted. Let N (k  r f ,  be the counting function for poles of f(z) with multiplicities  k ... See full document

... some uniqueness theorems of two transcendental meromorphic functions with their nonlinear di ff erential polynomials sharing a small ... See full document

... and uniqueness of com- plex difference polynomials of meromorphic ...of meromorphic functions are used (see [, ...a meromorphic function f , we use S(r, f ) to denote any ... See full document

... two meromorphic functions. We say that a(z) is a small function with respect to f(z) 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 ... See full document

... a meromorphic function always means meromorphic in the whole complex plane, and c always means a nonzero ...of meromorphic functions such as T(r, f ), m(r, f ), N(r, f ) and N(r, f ) as ... See full document

... non-constant meromorphic functions, , n k be two positive integers with n > + k 2 , and let P w ( ) be defined as in ...a small function with respect to f with finitely many zeros and ...g ... See full document

... Recently, a number of papers have focused on the Nevanlinna theory with respect to difference operators; see, e.g., the papers [, ] by Chiang and Feng and [, ] by Halburd and Korhonen. Then, many authors started to ... See full document

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

... non-constant meromorphic functions, and α ( ≡ 0, ∞ ) be a small function of f and ...a)g’ share a IM for a non-zero constant a, then either f ≡ g or f ≡ ... See full document

... small functions. Theorem 3 ([2]) Let f be a nonconstant entire function; let a ≡ 0 be a small function related to f ; and let k ≥ 2 be a positive ...(k+1) share a CM, then f ≡ f ... See full document

... of uniqueness of functions which are meromorphic in a multiply-connected domain–k-punctured complex plane ...characterized function T (r, f ) of meromorphic function and ... See full document

... of meromorphic functions in the open com- plex plane C; in , by considering the unicity of an entire function f and its first order derivative f , Rubel and Yang [] showed that f ≡ f when they ... See full document

... the functions f and g have the same simple one-points, there exists a mero- morphic function α such that α = 0 when f − 1 has a simple zero and α has no simple zero where f = 1 and g = α( f − 1) + ...the ... See full document

... a meromorphic function always mean a function which is meromorphic in the whole complex plane C ...of meromorphic functions as explained in ...nonconstant meromorphic ... See full document

... g(z) share the value a CM (counting multiplicities) and if they coincide in locations only we say that f (z) and g(z) share a IM (ignoring multiplic- ... See full document

... DOI: 10.4236/am.2017.88084 1118 Applied Mathematics outside of a possible exceptional set of r with finite logarithmic measure. In addition, the notation ρ ( ) f is the order of growth of f . Let meromorphic ... See full document

... It is well known that if f and g share four distinct values CM, then f is a fractional transformation of g. In 1997, corresponding to one famous question of Hayman, C. C. Yang and X. H. Hua showed the similar ... See full document

... tained f − 1 . So we expended Xiaomin Li and Zhitao Wen’s theorem. In 2008, Lianzhong Yang and Jilong Zhang proved the following theorems: Theorem A [4] Suppose f is a non-constant entire function, n ≥ 7 is a ... See full document

... can be relaxed. In this paper we investigate this problem and prove the following result. Theorem . Let F be a family of meromorphic functions defined in D, k be a positive integer, let h(z) be a ... See full document

... nonconstant meromorphic functions, and let a be a complex ...g(z) share a CM (IM) provided that f (z) – a and g(z) – a have the same zeros counting multiplicity (ignoring ... See full document