[PDF] Top 20 Uniqueness of Transcendental Meromorphic Functions with Their Nonlinear Differential Polynomials Sharing the Small Function

... 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 for a set of r of finite linear ...A ... 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

... 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 transcendental meromorphic function f of finite order, herein and hereinafter, c is a nonzero complex constant and a(z) is small function with respect to f , Liu et ...difference ... 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 ... See full document

... a transcendental meromorphic function such that its order of growth ρ(f ) is not an integer or infinite, and let c ∈ C be a constant such that f (z +c) ≡ f ... See full document

... Theorem E. Let f and g be two non-constant meromorphic functions, and α ( ≡ 0, ∞ ) be a small function of f and g. Let n and m(≥ 2) be two positive integers with n > max {4, 4m + 22 - 5Θ(∞, ... See full document

... The uniqueness theory of meromorphic functions mainly studies conditions under which there is a unique function satisfying the given ...two meromorphic functions while their ... 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 ... See full document

... 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

... two transcendental entire functions or both f and g are ...are transcendental entire functions, using N r f ( , ) = 0, N r g ( , ) = 0 and similar arguments as in the proof of Theorem 1, we ... See full document

... As a simple application of his own value distribution theory, Nevanlinna proved that a non-constant meromorphic function is uniquely determined by the inverse image of 5 distinct values (including the ... See full document

... meromorphic functions defined in D, all of whose zeros have multiplicity at least k + 1. If h(z) – 1 has at least two distinct zeros, h(f (k) ) + H(f ,f ,. . . ,f (k) ) – 1 has at most one distinct zero in D ... See full document

... Let f(z) and g(z) be two meromorphic functions, and let a(z) be a small function with respect to f(z) and g(z). We say that f(z) and g(z) share a(z) IM, provided that f(z) - a(z) and g(z) - ... See full document

... On transcendental meromorphic solutions of certain type of nonlinear algebraic differential equations Zhang Advances in Difference Equations (2016) 2016 300 DOI 10 1186/s13662 016 1030 0 R E S E A R C[.] ... See full document

... a meromorphic or an entire function sharing one small function with its derivative with weighted shared method and obtained the following result, which answered the open questions posed ... See full document

... the uniqueness of meromorphic functions sharing some finite sets in a special multiply-connected region—k-punctured complex plane— and obtained an analog of Nevanlinna’s famous five-value ... See full document

... a transcendental meromorphic function and n ∈ N, then f n f 0 takes every finite non-zero value infinitely often which means that the Picard exceptional value of f n f 0 may only be ... See full document

... w z + w z − = R z w z , (1.1) where R ( z ) is a nonzero rational function and m ∈ ± ± { 2, 1,0 } The Equation (1.1) comes from the family of Painlevé III equations which are given by Ron- kainen in [3] when he ... See full document

... holomorphic function in D, and the multiplicity of its all zeros is at most ...of meromorphic functions in D, the multiplicity of all zeros and poles of f ∈ F is at least max { k  + d + , k + ...of ... See full document