[PDF] Top 20 Normal families of meromorphic functions sharing values or functions

... of meromorphic func- tions in D, the multiplicity of all zeros and poles of f ∈ F is at least k + 2d + ...of functions f and g in F , f (k) and g (k) share p(z) in D, then F is normal in ...of ... See full document

... 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

... of meromorphic functions sharing values with their shifts or difference operators has become a subject of great interest ...value sharing problems for shifts of meromorphic ... 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

... Wang, YF, Fang, ML: Picard values and normal families of meromorphic functions with multiple zeros.. Schiff, J: Normal Families.[r] ... See full document

... can be relaxed. In this paper we investigate this problem and prove the following result. Theorem . Let F be a family of meromorphic functions defined in D, k be a positive integer, let h(z) be a ... See full document

... of meromorphic functions in a domain is normal if every function shares three distinct finite complex numbers with its first derivative ...shared values have emerged; for instance, see ... See full document

... Theorem 1.1 Let f be a nonconstant meromorphic function of finite order, let c be a con- stant such that f (z + c) – f (z) ≡ 0, and let a, b be two distinct nonzero finite constants. Suppose L r c f and f (z) share ... See full document

... 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

... Theorem 1.2 . Let f and g be two nonconstant meromorphic functions, whose zeros are of multiplicities at least k, where k is a positive integer. Let n >max{2k - 1, k + 4/k + 4} be a positive integer. If ... See full document

... Lemma 2.10 [15] Let f and g be non-constant meromorphic functions, , n k be two positive integers with n > + k 2 , and let P w ( ) be defined as in (1.1), a z ( ) ( ≡ ∞ / 0, ) be a small function with ... See full document

... Let fz and gz be two nonconstant meromorphic functions in the whole complex plane C, and let a be a finite complex value or function. We say that f and g share a CM or IM provided that f − a and g − a have ... See full document

... Let f and g be two non-constant meromorphic func- tions in the complex plane. It is assumed that the reader is familiar with the standard notations of Nevanlinna’s theory such as T r f  ,  , m r f  ,  , N r f ... 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

... a meromorphic function of order ρ ( < ρ < ∞), we say that a is an exceptional value in the sense of Borel (evB for short) for f for the distinct zeros if ρ(a, f ) < ... See full document

... Recently, some well-known facts of the Nevanlinna theory have been extended for the differences of meromorphic functions (see [5, 6, 9–11, 14–18]). For the existence on the fixed points of differences, Cui and ... See full document

... two meromorphic functions defined in C, there are many uniqueness theorems when they share small functions az is called a small function of fz if T r, az oT r, f r → ∞ see ...small functions ... See full document

... It should be mentioned that in the case of rational matrix functions G there is a well known parametrization of all optimal solutions of the matrix Nehari-Takagi problem in state space t[r] ... See full document

... for some α ( 0 ≤ α < 1 ) . We say that f (z) is in the class C (α) of such functions. The class ∗ (α) and various other subclasses of have been studied rather exten- sively by Nehari and Netanyahu [9], Clunie ... See full document

... The meromorphic function mentioned in this paper refers to the meromorphic function over the entire complex plane. Let f and g be two non-constant mero- morphic functions. E ⊂ ( 0, ∞ ) means Linear ... See full document