# On uniqueness of two meromorphic functions sharing a small function

## TL;DR

This paper studies the uniqueness of meromorphic functions sharing a small function, extending previous results by considering differential polynomials and correcting earlier errors, with implications for future research.

## Contribution

It extends and improves existing uniqueness results for meromorphic functions sharing small functions, including corrections of prior mistakes and new open questions.

## Key findings

- Extended the class of functions sharing small functions.
- Reduced the lower bound of n in the main theorems.
- Corrected previous errors in the literature.

## Abstract

In this paper, we have investigated the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing a small function. Our results radically extended and improved the results of Bhoosnurmath-Pujari and Harina - Anand not only by sharing small function instead of fixed point but also reducing the lower bound of $ n $. The authors Harina-Anand made plenty of mistakes in their paper. We have corrected all of them in a more convenient way. At last some open questions have been posed for further study in this direction.