MathDB
Miklós Schweitzer 1959- Problem 9

Source:

November 8, 2015
college contests

Problem Statement

9. Let f(z)=zn+a1zn−1+⋯+anf(z)= z^n +a_1 z^{n-1}+\dots + a_n be a polynomial over the field of the complex numbers and let EfE_f denote the closed (not necessarily connected) domain of complex numbers zz for which ∣f(z)∣≤1\mid f(z) \mid \leq 1. Show that there exists a point z0∈Efz_0 \in E_f such that ∣f′(z0)∣≥n\mid f'(z_0) \mid \geq n. (F. 5)
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