Weighted Set Sharing and Uniqueness of Meromorphic Functions

Abstract

In this paper, we study the uniqueness problem of meromorphic functions sharing a set of small functions and proved that under certain essential conditions $P[f]=tp(f)$ for some $t$ such that $t^m=1$ ($m$ is a positive number), where $P[f]$ is a differential polynomial in $f$ and $p(z)$ is a polynomial in $z$ of degree at least one such that $p(0)=0$. Our results generalizes the results due to Zhang and Lü}, Banerjee and Majumder, Bhoosnurmath and Kabur, and Charak and Lal.