Meromorphic functions in the unit disc that share values in an angular domain

Abstract

In this paper, we investigate the uniqueness of meromorphic functions in the unit disc and consider the relation between the Borel points and shared-values of meromorphic functions in an angular domain.

Nevanlinna’s Five Values Theorem on Annuli

“…Mao and H.Y. Xu (including [9][10][11]) investigated the shared value of meromorphic functions in the unit disc; J.H. Zheng, Q.C.…”

“…Mao and H.F. Liu [10] gave a different method to investigate the uniqueness problem of meromorphic functions in the unit disc and obtained the following results. Theorem 1.2.…”

The uniqueness problem for meromorphic functions in the unit disc sharing values and a set in an angular domain

“…After their work, the uniqueness of meromorphic functions with shared values in the whole complex plane attracted many investigations (see [18]). It is an interesting topic to investigate the uniqueness with shared values in the remaining part of the complex plane removing an unbounded closed set, see [2], [3], [8]- [10], [15]- [17], [21], [22]. In [21], Zheng studied the uniqueness problem under the condition that five values are shared in some angular domain in C. Zheng J. H. [22], Cao T. B. and Yi H. X.…”

On meromorphic functions for sharing two sets and three sets in m-punctured complex plane

“…Around 2000s, Fang, Zheng and Mao investigated the uniqueness of meromorphic functions in the unit disc and some angular domain, and obtained some important results (see [4][5][6][7][8][9]). …”