Lower bound in the Bernstein inequality for the first derivative of algebraic polynomials
We prove that |p′(x)|, where p runs over the set of all algebraic polynomials of degree not higher than n ≥ 3 bounded in modulus by 1 on [−1, 1], is not lower than \( ( n - 1 ) /( n - 1 ) 1 - x^2 . 1 - x^2 \) for all x ∈ (−1, 1) such that \( | x | olimits_k = 0^[ n /n 2 . 2 ] [ 2k + 1 2( n - 1 ) π, 2k + 1 2n π ] \)., number=5, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Podvysotskaya, A. I., year=2009, month=May, pages=711–715