The Bernstein Constant and Polynomial Interpolation at the Chebyshev Nodes Original Research Article

In this paper, we establish new asymptotic relations for the errors of approximation in Lp[−1,1], 00, by the Lagrange interpolation polynomials at the Chebyshev nodes of the first and second kind. As a corollary, we show that the Bernstein constantBλ,p≔limn→∞nλ+1/p infck∥∣x∣λ−∑k=0nmckxk∥Lp[−1,1] is finite for λ>0 and p∈13,∞).