# zbMATH — the first resource for mathematics

Note on Bernstein’s inequality for the third derivative of a polynomial. (English) Zbl 1060.30003
Summary: Given a polynomial $$p(z)= \sum^n_{j=0} a_j z^j$$, we give the best possible constant $$c_3(n)$$ such that $$\| p'''\|+ c_3(n)|a_0|\leq n(n- 1)(n-2)\| p\|$$, where $$\|\;\|$$ is the maximum norm on the unit circle $$\{z: |z|= 1\}$$. Most of the computations are done with a computer.
##### MSC:
 30A10 Inequalities in the complex plane 26D05 Inequalities for trigonometric functions and polynomials 26D10 Inequalities involving derivatives and differential and integral operators 30C10 Polynomials and rational functions of one complex variable
##### Keywords:
Bernstein’s inequality; unit circle
Full Text: