[PDF] Top 20 On the value distribution and uniqueness of difference polynomials of meromorphic functions

... transcendental meromorphic function f of finite order, a nonzero complex con- stant c and α(z) ∈ S(f ), Liu et ...difference polynomials of meromorphic functions and obtained: If n ≥ , then f ... See full document

... In the following, we will consider the zeros of other difference polynomials. Using the similar method of the proof of Theorem 1.2 below, we also can obtain the following results. Theorem 1.4. Let f be a ... See full document

... a meromorphic function play key roles in the construction and applications of classical Nevanlinna ...studying difference equations in the complex ...on difference operator. Bergweiler and Langley [ ... See full document

... In recent years, there has been an increasing interest in studying difference equations, difference products and q-differences in the complex plane C , and a number of papers (including [–]) have focused on the ... 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

... Nevanlinna value distribution theory of meromorphic func- tions (see [, ...mean meromorphic in the whole complex plane ...a meromorphic function f (z), λ(f ) to denote the exponents of ... See full document

... the value distribution theory [4]. For any nonconstant meromorphic function f (z) on the complex plane C, we denote by S(r, f ) any quantity satisfying S(r, f ) = o(T(r, f )) as r → ∞ except possibly ... See full document

... the value distribution of different expressions of meromorphic functions and obtained lots of important theorems (see ...of meromorphic functions and their deriva- tives, and he ... See full document

... the value distribution of meromorphic functions with respect to differ- ence has become a subject of some interests (see [1, 3–5, 7–10, ... See full document

... [7] Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J. and Zhang, J. (2009) Value Sharing Results for Shifts of Meromorphic Functions, and Sufficient Conditions for Periodicity. Journal of ... 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

... nonconstant meromorphic function on ℂ ...Nevanlinna value distribution theory such as T (r, f ), m(r, f ), N(r, f ) (see, ...A meromorphic function a is called a small function with respect to ... 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 ... See full document

... Copyright © 2014 Xinhua Shi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the ... See full document

... the value distribution of difference polynomial and obtain the following result, which improves a recent result of ...transcendental meromorphic function of finite order σ , c be a nonzero constant, ... 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

... a meromorphic function in the complex plane C and a ∈ C , we use the follow- ing notations frequently used in Nevanlinna theory (see [–]): m(r, f ), N(r, f ), m(r, a) = m(r, f–a  ), N(r, a) = N(r, f –a  ), ... See full document

... the value a CM counting multiplicities if f − a and g − a have the same zeros with the same multiplicities, and we say that f and g share the value a IM ignoring multiplicities if we do not consider the ... See full document

... In this paper, we study the uniqueness of meromorphic functions whose differential polynomial share a non-zero finite value. The results in this paper improve some results given by Fang (Math. ... See full document

... a uniqueness theorem of meromorphic functions whose some nonlinear differential shares 1 IM with powers of the meromor- phic functions, where the degrees of the powers are equal to those of ... See full document