[PDF] Top 20 Generalization of Uniqueness Theorems for Entire and Meromorphic Functions

... Abstract In this paper, we deal with the uniqueness problems on entire and meromorphic functions concerning differential polynomials that share fixed-points.. Moreover, we generalise and[r] ... See full document

... Wiman - Valiron theory for difference equations of entire functions of small growth. Growth estimates for the difference analogue of logarithmic derivative f(z+c) f(z) were given by Halburd and Korhonen [1] ... See full document

... the theorems, we know that either both f and g are two transcendental entire functions or both f and g are ...transcendental entire functions, using N r f ( , ) = 0, N r g ( , ) = 0 and ... 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 ... See full document

... small functions. Theorem 3 ([2]) Let f be a nonconstant entire function; let a ≡ 0 be a small function related to f ; and let k ≥ 2 be a positive ...of meromorphic functions with respect to ... See full document

... The uniqueness of meromorphic functions sharing values with their shifts or difference operators has become a subject of great interest ...of meromorphic functions and obtained some ... 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 derivatives ... See full document

... of meromorphic functions occupies one of the central places in complex ...important uniqueness theorems in the complex plane to the subset X (including the unit disc, the angular domain, the ... See full document

... the uniqueness problems on the case that shifts or differ- ence polynomials of two entire functions share a small ...the uniqueness problems of difference operators of meromorphic ... 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 ... 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

... some uniqueness theorems of two transcendental meromorphic functions with their nonlinear di ff erential polynomials sharing a small ... See full document

... Remark 1.3. The proof of Theorem E contains some mistakes: for example, one cannot get formulas 6.9 and 6.10 in 8. Therefore, the last inequality in page 1203 of 8 does not hold. So, Theorem E will not stand. Similarly, ... See full document

... and where in the following, T (r, f ) is the characteristic function of Nevanlinna. On the basic of Definition 1.1, recently in [17] , X. Shen, J. Tu and H. Y. Xu introduced the new concept of [p, q] − ϕ order of ... See full document

... Let denote the complex plane, and let fz be a nonconstant meromorphic function in . It is assumed that the reader is familiar with the standard notion used in the Nevanlinna value distribution theory such as the ... See full document

... The bounds obtained are used to derive the distortion theorems, the covering theorems and the radii of convexity for the classes of regular or meromorphic starlike functions associated w[r] ... See full document

... a ∈ C  ∞ , we say that f z ( ) and g z ( ) share a CM (counting multiplicities) if f z ( ) − a , g z ( ) − a have the same zeros with the same multiplicities and we say that f z ( ) and g z ( ) share a (ignoring multip- ... 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. Appl. ... See full document

... of entire functions using relative ...of entire and meromorphic functions in terms of their relative order which improves some results of Datta and Biswas ... 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 infinity) IM. ... See full document