[PDF] Top 20 Meromorphic functions that share a polynomial with their difference operators

... 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

... 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

... Abstract In this paper we deal with the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share a small function.. Ke[r] ... See full document

... 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 the non- linear differential ... See full document

... Recently, the difference analog of Nevanlinna theory has been established; see, e.g. [2, 7–10, 14]. Many researchers ([1, 12, 13, 15–17], etc.) started to consider the uniqueness of meromorphic functions ... See full document

... of meromorphic functions which involves differential polynomial sharing ...a polynomial with degree at least 2, and H(f, f , ...differential polynomial with γ | H < k + ... See full document

... nonconstant meromorphic functions for some a ∈ C ∪ ...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 ... 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

... 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 → ...differential polynomial in f . Suppose f n and P[ f ] ... See full document

... Abstract. With the aid of weighted sharing method we study the uniqueness of meromorphic (entire) functions concerning some general nonlinear differen- tial polynomials sharing fixed points. The results of ... See full document

... two meromorphic functions f (z) and g(z), and a ∈ S(f ) ∪ S(g) ∪ {∞} , we say that f (z) and g(z) share a CM when f (z) – a and g(z) – a have the same zeros counting ... See full document

... entire functions of finite order sharing a periodic small function to f ...of meromorphic functions of finite order sharing a polynomial, which is a more popular ... See full document

... of meromorphic functions is an important part of Nevanlinna ...of meromorphic functions are the five-value theorem and four-value theorem due to Nevanlinna ...two meromorphic ... See full document

... two meromorphic functions, and let a(z) be a small function with respect to 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 multiplicities), ... 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

... A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity like a polynomial ...a ... See full document

... a meromorphic function play key roles in the construction and applications of classical Nevanlinna ...studying difference equations in the complex ...of difference operators that can be viewed ... See full document

... a meromorphic function f (z) is of finite order, then the order of n(r, f = a) equals the exponent of convergence of a-points of f ...for meromorphic functions of finite logarithmic order also ... See full document

... [1] H. Airault and J. Ren, “An algebra of differential operators and generating functions on the set of univalent functions,” Bulletin des Sciences Math´ematiques, vol. 126, no. 5, pp. 343–367, 2002. ... See full document

... (2) Theorem 1.1 does not remain valid when n = 1. For example, f (z) = e z + 1 and f (z + c) = e z+c + 1, where c ≠ 2 π i. Clearly, f(z) and f (z + c) share 1 and ∞ CM, however, f (z) ≠ ω f (z + c) for ω n = 1. ... See full document