[PDF] Top 20 Uniqueness problems on entire functions that share a small function with their difference operators

... meromorphic functions, and let a(z) be a small function of f (z) and ...g(z) share a(z) IM, provided that f (z) – a(z) and g(z) – a(z) have the same zeros ignoring ...g(z) share a(z) ... 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 ... 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 ... See full document

... Firstly, we claim that f (z) cannot be a non-polynomial rational function. Otherwise, sup- pose that f (z) = a(z) b(z) , where a(z) and b(z) are two co-prime polynomials. By equation (2.1), we can get that f , n c ... See full document

... the uniqueness of f(z) and its shift f(z+c), where c is a non-zero complex ...sharing problems for the shifts of meromorphic functions and obtained many results as ... See full document

... 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] ...non-linear ... 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

... It is natural to pose the question: what can be said on replacing shared values in Theo- rems C–E by shared small functions. Concerning this question, we obtain the following results which extend Theorems ... 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

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

... meromorphic function always means meromorphic in the whole complex plane, and c always means a non-zero ...phic function f (z), we use the basic notations of the Nevanlinna theory (see [11, 21, ... See full document

... the uniqueness problem when an entire function shares 0 CM and nonzero complex constant a IM with its difference ...they share two distinct complex constants a ∗ CM and a IM under some ... See full document

... meromorphic functions and let a be a finite com- plex ...g share a CM, provided that f - a and g - a have the same zeros with the same ...g share a IM, pro- vided that f - a and g - a have the same ... See full document

... Fractional q-difference (q-fractional difference) equations are regarded as the fractional analog of q-difference equations. The topic of q-fractional equations has attracted the at- tention of many researchers. The details ... See full document

... for t ∈ {a + µ , a + µ + 1, . . .} := N a+µ . Also define the µ th fractional difference for µ > 0 by ∆ µ f (t) := ∆ N ∆ µ−N f (t), where t ∈ N a+µ and µ ∈ N is chosen so that o ≤ N − 1 < µ ≤ N. Lemma 1.3. ... See full document

... meromorphic function mentioned in this paper refers to the meromorphic function over the entire complex ...CM share a ...IM share a ... See full document

... Recently, the difference variant of the Nevanlinna theory has been established indepen- dently in [–]. Using these theories, value distributions of difference polynomials have been studied by many papers. For example, ... See full document

... hypergeometric functions immediately reduce to their original ...these functions by using the integral representation of the new beta function (1) in the same way as in [1–6, ... See full document

... In the first time, we gave full classification of the group. Number of classes of the classification is k-1. We named them self-m-al at 2≤m≤k. We built the theory of self-k-al functions and proved 10 important ... See full document