MathDB
Miklos Schweitzer 1970_8

Source:

October 22, 2008
algebrapolynomialreal analysisreal analysis unsolved

Problem Statement

Let πn(x) \pi_n(x) be a polynomial of degree not exceeding n n with real coefficients such that |\pi_n(x)| \leq \sqrt{1\minus{}x^2} \;\textrm{for}\ \;\minus{}1\leq x \leq 1 \ . Then |\pi'_n(x)| \leq 2(n\minus{}1). P. Turan