A Note On Uniqueness Of Meromorphic Functions And Their Derivatives Sharing Two Sets

TL;DR

This paper investigates the uniqueness of meromorphic functions and their derivatives when sharing two sets, affirmatively answering a specific open question and providing examples to demonstrate the sharpness of conditions.

Contribution

It extends previous work by affirmatively resolving a question on the uniqueness of meromorphic functions sharing sets with their derivatives and illustrates the sharpness of conditions with examples.

Findings

Confirmed the uniqueness of meromorphic functions sharing two sets with derivatives

Provided examples demonstrating the sharpness of conditions in the main theorem

Extended previous results on the sharing of sets by meromorphic functions

Abstract

In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively. Moreover, we exhibit some examples to show the sharpness of some conditions used in our main result.