[PDF] Top 20 Value Distribution and Uniqueness Theorems for Difference of Entire and Meromorphic Functions

... for difference equations of entire functions of small ...the difference analogue of logarithmic derivative f(z+c) f(z) were given by Halburd and Korhonen [1] ...order meromorphic ... See full document

... in value distribution of difference operators of meromorphic functions (see ...the uniqueness results of difference polynomials of meromorphic functions, ... See full document

... : Value distribution of the difference opera- tor, Advances in Difference equations, ...X.H.: Uniqueness and value sharing of meromorphic functions, ... 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 ...the value distribution of ... See full document

... A meromorphic (respectively entire) function always means a non-constant function meromorphic (respectively analytic) in the complex ...of value distribution is concerned with the ... See full document

... fundamental theorems and the standard notations of the Nevanlinna value distribu- tion theory of meromorphic functions will be used (see ...a meromorphic function f (z), we use S(r, f ) ... 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 conclusions ... See full document

... following theorems: Theorem A [4] Suppose f is a non-constant entire function, n ≥ 7 is a posi- tive integer, if f n and ( ) f n ′ CM share 1, then f n = ( ) f n ′ ... See full document

... The uniqueness of meromorphic functions sharing values with their shifts or difference operators has become a subject of great interest ...the value sharing problems for shifts of ... See full document

... of Meromorphic functions is an important part of Nevan- linna ...to difference operators. This has lead to development of difference counterparts of many central results of Nevanlinna theory ... See full document

... A meromorphic function α(z) is called a small function with respect to f (z), if T(r, α) = S(r, f ), where S(r, f ) denotes any quantity satisfying S(r, f ) = o(T (r, f )) as r → ∞ outside a possible exceptional ... See full document

... and uniqueness of com- plex difference polynomials of meromorphic ...Nevanlinna value distribution theory of meromorphic functions are used (see [, ...a meromorphic ... See full document

... non-constant meromorphic functions, n ≥ 11 an integer and a Î C - ...the value a CM, then either f = tg for a constant t with t n+1 = 1 or g(z) = c 1 e cz and f(z) = c 2 e -cz , where c, c 1 and c 2 ... See full document

... We recall the following result by Xu et al. [25] or Zhang and Li [26], respectively. Theorem D. Let f be a transcendental meromorphic function, n(≤ 2), k be two posi- tive integers. Then f n f (k) takes every ... See full document

... Theorem A: Let w ( z ) and u ( z ) be two nonconstant meromorphic functions. If w ( z ) and u ( z ) share 5 values IM (4 values CM, respectively) in the extended complex plane, then w z ( ) ≡ u z w z ( ) ( ... See full document

... Uniqueness of Meromorphic Functions Concerning Differential Monomials* Hui Huang, Bin Huang College of Mathematics, Changsha University of Science and Technology, Changsha, China E-mail:[r] ... See full document

... Theorem D. Let f be a non-constant meromorphic function, n be a positive integer and a(6≡ 0, ∞) be a meromorphic function satisfying T (r, a) = o(T (r , f )) as r → ∞. Let P[ f ] be a non- constant ... See full document

... constant meromorphic function in the whole complex plane  ...of value distribution theory: T r f ( , ) ( , m r f , ) ( , N r f , ) ( , N r f , ) ,  (see [2] ... See full document

... Deparment of Mathematics, Karnatak University, Dharwad, Karnataka state, India E-mail address : [email protected].[r] ... See full document

... two meromorphic functions, and let a(z) be a small function of f (z) and ...on meromorphic functions sharing small functions with their derivatives is an important topic of ... See full document