POINTWISE ESTIMATE FOR ALGEBRAIC POLYNOMIAL APPROXIMATION

Let f(x)∈C-1, 1], and ∏_n be the class of algebraic poly-nomials of degree n. It is well known that algebraic polynomialapproximation can be improved near the end points of the interval-1, 1]. This fact was first observed by A. F. Timan, and laterJ. Brudnyi proved that for any positive integer k, there is aρ_n(x)∈∏_n such that