Differential rings of meromorphic functions

Uniqueness of meromorphic functions ans Q-differential polynomials sharing small functions

‎The paper concerns interesting problems related to the field of Complex Analysis‎, ‎in particular, Nevanlinna theory of meromorphic‎ ‎functions‎. ‎We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a‎ ‎small function‎. ‎Outside‎, ‎in this paper‎, ‎we also consider the uniqueness of $q-$ shift difference‎ - ‎differential polynomials‎ ‎of mero...

Uniqueness of Meromorphic Functions and Differential Polynomials

Let f be a nonconstant meromorphic function defined in the whole complex plane . It is assumed that the reader is familiar with the notations of the Nevanlinna theory such as T r, f , m r, f ,N r, f , and S r, f , that can be found, for instance, in 1–3 . 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 mul...

Uniqueness of Meromorphic Functions Concerning Differential Monomials

Considering the uniqueness of meromorphic functions concerning differential monomials ,we obtain that, if two non-constant meromorphic functions   f z and   g z satisfy     1, 1, n n k k E f f E g g    , where k and n are tow positive integers satisfying 3 k  and 11 n  , then either     1 2 , cz cz z z f c e g c e    where 1 c , 2 c , c are three constants, satisfying   1 ...

On the Configuration of Herman Rings of Meromorphic Functions

We prove some results concerning the possible configurations of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period and give a sufficient condition for a configuration to be realizable.

Differential Polynomial Rings of Triangular Matrix Rings