The Bernstein constant and polynomial interpolation at the Chebyshev nodes

In this paper, we establish new asymptotic relations for the errors of approximation in L-p [-1,1], 0 <p ≤ ∞, of \x\(λ), λ > 0, by the Lagrange interpolation polynomials at the Chebyshev nodes of the first and second kind. As a corollary, we show that the Bernstein constant [GRAPHICS] is finite for lambda > 0 and p is an element of (1/3, infinity). (C) 2002 Elsevier Science (USA).