[PDF] Top 20 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

... find normality criteria from the point of shared ...of meromorphic functions in a domain is normal if in which every function shares three distinct finite complex numbers with its first ...about ... See full document

... find normality criteria from the point of view of shared val- ...of meromorphic functions in a domain is normal if every function shares three distinct finite complex numbers with its first derivative ... See full document

... Let f be a nonconstant meromorphic function in the complex plane C. We shall use the standard notations in Nevanlinna’s value distribution theory of meromorphic functions such as T r, f , Nr, f , and ... See full document

... nonconstant meromorphic functions in the whole complex plane C, and let a be a finite complex value or ...g share a CM or IM provided that f − a and g − a have the same zeros counting or ignoring ... See full document

... 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) share the ... See full document

... 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 ...(z) share three distinct values a, b, ∞ CM, ... See full document

... non-constant meromorphic functions and let a be a finite com- plex ...g share a CM, provided that f - a and g - a have the same zeros with the same ...g share a IM, pro- vided that f - a and g ... See full document

... 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 those of the non- linear ... See full document

... g(z) share the value a CM (counting multiplicities) and if they coincide in locations only we say that f (z) and g(z) share a IM (ignoring multiplic- ... See full document

... g share four distinct values CM, then f is a fractional transformation of ...of differential polynomials when they share only one ... See full document

... ) 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- licities) if we do not ... See full document

... Given specific values of s in Theorems 3.1–3.3, we can compare n in the two conditions of n and s and see that the second condition is always better than the first one for s ≥ 3. For example, we consider (n – 4)s ≥ ... See full document

... some meromorphic functions on ...g share a CM provided the two meromorphic functions f – a and g – a have the same zeros with counting ... 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

... entire functions, and let n, m, k be three positive integers such that n > 5k 4m ...k share 1 IM, then either fz ≡ gz or f and g satisfy the algebraic equation Rf, g ≡ 0, where Rω 1 , ω 2 ω n 1 ω 1 − 1 m ... See full document

... nonconstant meromorphic functions for some a ∈ C ∪ ...g(z) share the value a CM (counting multiplicities), and if they coincide in locations only, we say that f (z) and g(z) share a IM ... See full document

... given meromorphic function f (z) with finite positive order and for any a ∈ C, the counting functions N(r, f = a) and n(r, f = a) both have the same order, the situation is different for functions of ... See full document

... It is natural to pose the question: what can be said on replacing shared values in Theo- rems C–E by shared small functions. Concerning this question, we obtain the following results which extend Theorems ... See full document

... Let ℂ denote the complex plane and f be a nonconstant meromorphic function on ℂ . We assume the reader is familiar with the standard notion used in the Nevanlinna value distribution theory such as T (r, f ), m(r, ... See full document