On meromorphic functions sharing two one-point sets and two three-point sets

Two Meromorphic Functions Sharing Sets concerning Small Functions

The main purpose of this paper is to deal with the uniqueness of meromorphic functions sharing sets concerning small functions. We obtain two main theorems which improve and extend strongly some results due to R. Nevanlinna, Li-Qiao, Yao, Yi, Thai-Tan, and Cao-Yi.

A Uniqueness Result Related to Meromorphic Functions Sharing Two Sets

With the help of a new unique range set we investigate the well known question of Gross and prove a uniqueness theorem on meromorphic functions sharing two sets. The result in this paper will improve and supplement some earlier results.

On Pre-θ-Open Sets and Two Classes of Functions

Uniqueness of derivatives of meromorphic functions sharing two or three sets

In the paper we consider the problem of uniqueness of derivatives of meromorphic functions when they share two or three sets and obtained five results which will improve all the existing results. Key word and phrases: Meromorphic functions, uniqueness, weighted sharing, derivative, shared set.

Homeomorphisms of Two-point Sets

Given a cardinal κ ≤ c, a subset of the plane is said to be a κ-point set if and only it it meets every line in precisely κ many points. In response to a question of Cobb, we show that for all 2 ≤ κ, λ < c there exists a κ-point set which is homeomorphic to a λ-point set, and further, we also show that it is consistent with ZFC that for all 2 ≤ κ < c, there exists a κ-point set X such that for ...