[PDF] Top 20 Notes on the uniqueness of meromorphic functions concerning differential polynomials

... 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

... 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

... 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

... In recent years, there has been an increasing interest in studying difference equations, difference products and q-differences in the complex plane C , and a number of papers (including [–]) have focused on the value ... See full document

... It follows from the proof of Theorems 1.11–1.14 that if “z” is replaced by “a(z)” in The- orems 1.11–1.14, where a(z) is a meromorphic function such that a ≡ 0, ∞ and T(r,a) = o { T (r, f ), T(r,g ) } , then the ... 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 to ... See full document

... Let f and g be two nonconstant meromorphic functions. Let a be a finite complex number. We say that f and g share the value a CM counting multiplicities if f − a and g − a have the same zeros with the same ... See full document

... Uniqueness of Meromorphic Functions Concerning Differential Monomials* Hui Huang, Bin Huang College of Mathematics, Changsha University of Science and Technology, Changsha, China E-mail:[r] ... See full document

... It is well known that if f and g share four distinct values CM, then f is a fractional transformation of g. In 1997, corresponding to one famous question of Hayman, C. C. Yang and X. H. Hua showed the similar conclusions ... 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

... two meromorphic functions f and g, if f n f (k) and g n g (k) have the same fixed points or share one nonzero complex number, where n and k are positive numbers? In this direction, we will ... See full document

... Later on, many mathematicians studied the polylogarithm function such as Euler, Spence, Abel, Lobachevsky, Rogers, Ramanujan, and many others [4], where they discovered many functional identities by using polylogarithm ... See full document

... Firstly, we claim that f (z) cannot be a non-polynomial rational function. Otherwise, sup- pose that f (z) = a(z) b(z) , where a(z) and b(z) are two co-prime polynomials. By equation (2.1), we can get that f , n c ... See full document

... Deparment of Mathematics, Karnatak University, Dharwad, Karnataka state, India E-mail address : [email protected].[r] ... See full document

... A recent increment to uniqueness theory has been to considering weighted shar- ing instead of sharing IM/CM which implies a gradual change from sharing IM to sharing CM. This notion of weighted sharing has been ... See full document

... nonconstant meromorphic functions; a meromorphic function az / ≡ ∞ is called a small functions with respect to f provided that T r, a Sr, f ... See full document

... Denote by S(r, f ) any quantity satisfying S(r, f ) = o(T (r, f )) as r → ∞ , possibly outside of a set of r with a finite logarithmic measure. A meromorphic function a(z) is said to be a small function of f (z) if ... 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) - a(z) have the ... See full document

... the uniqueness of meromorphic functions with shared values in the whole complex plane attracted many investigations see ...of uniqueness of a function meromorphic in a precise subset of ... See full document

... Let f be a transcendental entire function. As for the value distribution of dif- ferential polynomial f n (f − 1)f 0 , Fang [15] showed that f n (f − 1)f 0 assumes every non-zero value a ∈ C infinitely often for n ≥ 4. ... See full document