On some generalisations of Brown's conjecture

Let P be a complex polynomial of the form P(z)=z\displaystyle\prod_{k=۱}^{n-۱}(z-z_{k}),where |z_k|\ge ۱,۱\le k\le n-۱ then P^\prime(z)\ne ۰. If |z|<\dfrac {۱}{n}. In this paper, we present some interesting generalisations of this result.

Keywords:

Critical points , Sendove's Conjecture , Coincidence theorem of walsh