Uniqueness of meromorphic functions that share Two Sets

TL;DR

This paper investigates the conditions under which two meromorphic functions are uniquely determined by sharing two finite sets, introducing a new concept of finite range sets in the complex plane.

Contribution

It introduces a novel type of finite range sets in the complex plane that characterize the uniqueness of meromorphic functions sharing these sets.

Findings

New finite range sets defined for meromorphic functions

Conditions established for uniqueness based on shared sets

Theoretical framework for function determination from shared sets

Abstract

In this note, we introduce a new kind of pair of finite range sets in $\mathbb{C}$ for meromorphic functions corresponding to their uniqueness, i.e., how two meromorphic functions are uniquely determined by their two finite shared sets.