On generalisation of Brown's conjecture

Let  P be the complex polynomial of the form P(z) = z \prod_{j=۱}^{n-۱}(z-z_{j}), with |z_{j}|\geq ۱, ۱ \leq j \leq n-۱. Then according to famous Brown's Conjecture p'(z) \neq ۰, for |z| < \frac{۱}{n}. This conjecture was proved by Aziz and Zarger [۱]. In this paper, we present some interesting generalisations of this conjecture and the results of several  authors related to this conjecture.

کلیدواژه ها:

Polynomial ، disk ، Zeros ، Derivative ، conjecture