Revisiting a General Property of Meromorphic Functions
نویسندگان
چکیده
The numbers of a-points of different classes of meromorphic functions have been widely studied for more than 120 years. As a culmination of similar studies, there arose classical Nevanlinna theory (1920s) and Ahlfors theory (1935). Clearly, further development should touch not only the numbers of a-points but also on their locations. Similar regularities were established nearly 30 years ago: they are the so-called proximity (or closeness) properties of a -points of meromorphic functions which describe mutual locations of a-points and imply simultaneously the key conclusions of Nevanlinna and Ahlfors theories. In the present paper we give a new, essentially simplified wording of one of the main versions of this property.
منابع مشابه
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...
متن کاملOn convolution properties for some classes of meromorphic functions associated with linear operator
In this paper, we defined two classes $S_{p}^{ast }(n,lambda ,A,B)$ and\ $ K_{p}(n,lambda ,A,B)$ of meromorphic $p-$valent functions associated with a new linear operator. We obtained convolution properties for functions in these classes.
متن کاملFive-value rich lines, Borel directions and uniqueness of meromorphic functions
For a meromorphic function $f$ in the complex plane, we shall introduce the definition of five-value rich line of $f$, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of $f$ ...
متن کاملOn uniqueness of meromorphic functions sharing five small functions on annuli
The purpose of this article is to investigate the uniqueness of meromorphic functions sharing five small functions on annuli.
متن کاملComposition operators and natural metrics in meromorphic function classes $Q_p$
In this paper, we investigate some results on natural metrics on the $mu$-normal functions and meromorphic $Q_p$-classes. Also, these classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, compact composition operators $C_phi$ and Lipschitz continuous operators acting from $mu$-normal functions to the meromorphic $Q_p$-classes are characte...
متن کامل