Distribution of Extreme Points of the Error Curve of Best Approximation by Incomplete Polynomials Original Research Article

Let Πn,m = {(x + 1)nPm(x) : Pm(x) ∈ Πm} be the set of incomplete polynomials of type (n, m) on [−1, 1]. We consider the distribution of the extreme points of the error curve in the best approximation of ƒ ∈ C[−1, 1] with ƒ(−1) = 0 by incomplete polynomials of type (n, m) on [−1, 1] and give a Kadec-type result for this setting. In particular, we improve the rate of convergence of the original Kadec result.