Value sharing of an entire function and its derivatives

Abstract

In this paper, when an entire function $f$ and the linear combination of its derivatives $L\left(f\right)$ with small functions as its coefficients share one value CM and another value IM is studied. We also resolved the question when an entire function $f$ and its derivative $f^{\prime }$ share two values CM jointly. Some of the results remain to be valid if $f$ is meromorphic and satisfying $N(r,f)=o\left(T\right(r,f\left)\right)$ as $r\to \infty$ and the values $a,$$b$ are replaced by small functions of $f\left(z\right)$.