[PDF] Top 20 5. ON MEROMORPHIC FUNCTIONS THAT SHARE A SMALL FUNCTION WITH ITS DERIVATIVES
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5. ON MEROMORPHIC FUNCTIONS THAT SHARE A SMALL FUNCTION WITH ITS DERIVATIVES
... In 2015, Jin-Dong Li and Guang-Xiu Huang [?] proved the following Theorem. Theorem G. Let f be a non-constant meromorphic function, k(≥ 1), l(≥ 0) be integers. Also let a ≡ a(z)(6≡ 0, ∞) be a ... See full document
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The partially shared values and small functions for meromorphic functions in a k punctured complex plane
... of meromorphic functions occupies one of the central places in complex ...for meromorphic functions in the unit disc; Zheng [11] in 2003 obtained the five-value theorem for meromorphic ... See full document
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Uniqueness of meromorphic functions concerning differential polynomials share one value
... non-constant meromorphic functions, and α ( ≡ 0, ∞ ) be a small function of f and ...a)g’ share a IM for a non-zero constant a, then either f ≡ g or f ≡ ... See full document
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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 ... See full document
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Uniqueness problems on entire functions that share a small function with their difference operators
... two 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) ... See full document
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Non real zeros of derivatives of meromorphic functions
... It would clearly be preferable to know whether Theorem 1.5 holds without hypotheses (c) and (d), but the present method does not deliver this, and in particular it seems difficult to exclude the possibility that f has ... See full document
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Uniqueness of Transcendental Meromorphic Functions with Their Nonlinear Differential Polynomials Sharing the Small Function
... transcendental meromorphic functions, a(z) ∈ S( f ) ∩ S(g ...g(z) share the function a(z) CM, espe- cially, we say that f (z) and g (z) have the same fixed points when a(z) = ...g(z) ... See full document
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13. Meromorphic functions that share fixed points with finite weights
... by meromorphic functions we will always mean meromorphic func- tions in the complex ...of meromorphic functions as explained in [10], [20] and ...stant meromorphic ... See full document
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Meromorphic functions sharing small functions with their linear difference polynomials
... 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
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23. Some Further results on the Unique Range Sets Of Meromorphic Functions
... In the last couple of years the concept of URSE, URSM and URSM-IM have caused an increasing interest among the researchers. The study is focused mainly on two problems: finding different URSM with the number of elements as ... See full document
12
Meromorphic functions that share four or three small functions with their difference operators
... Nevanlinna’s four-value theorem shows that if two non-constant meromorphic func- tions f and g share four distinct values CM, then f is a Möbius transformation of g. In [4], Gundersen constructed a ... See full document
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Unicity of Meromorphic Function Sharing One Small Function with Its Derivative
... nonconstant meromorphic functions; a meromorphic function az / ≡ ∞ is called a small functions with respect to f provided that T r, a Sr, f ...all small function of ... See full document
11
Some inequalities on meromorphic function and its derivative concerning small functions in an angular domain
... a meromorphic function from the whole plane to an angular ...of meromorphic functions of infinite order sharing some values in the Borel direction; in the same year, Zhang et ...of ... See full document
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Derivatives of meromorphic functions of finite order
... Carleman-Ahlfors theorem [2, 5, 10], there are finitely many such singularities. The following facts are related to the argument from [7, Section 4]. Let J be a polygonal Jordan curve in C \ {0} such that every ... See full document
14
Uniqueness of Meromorphic Functions with Their Nonlinear Differential Polynomials Share a Small Function
... 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
5
Normal families of meromorphic functions sharing one function
... of meromorphic functions in D, all of whose zeros have multiplicity at least ...of functions f and g in F, P(f )f (k) and P(g)g (k) share b in D, then F is ... See full document
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A quasinormal criterion of meromorphic functions and its application
... Theorem . Let k ≥ be an integer, let f (z) be a meromorphic function in C, and let α(z) = R(z)h(z) (≡ ), where h(z) is an elliptic function and R(z) is a rational function. Suppose that ... See full document
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Uniqueness of Meromorphic Functions Whose Differential Polynomials Share One Value
... tained f − 1 . So we expended Xiaomin Li and Zhitao Wen’s theorem. In 2008, Lianzhong Yang and Jilong Zhang proved the following theorems: Theorem A [4] Suppose f is a non-constant entire function, n ≥ 7 is a ... See full document
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Normality of meromorphic functions and differential polynomials share values
... meromorphic functions defined in D, all of whose zeros have multiplicity at least k + ...of functions f and g in F, h(f (k) ) + H(f, f , ...) share b in D, then F is normal in D, ... See full document
9
Growth and Complex Oscillation of Linear Differential Equations with Meromorphic Coefficients of [p,q] − ϕ Order
... with meromorphic coeffi- cients under some assumptions for [p, q] − ϕ order and we obtain some results which improve and extend some previous results of ... See full document
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