Some Erdös-type Convergence Processes in Weighted Interpolation

In 1943, P. Erdös [5] showed that if the interpolation point system X n C [-1, 1] (n ∈ N) such that the fundamental polynomials of Lagrange interpolation are uniformly bounded in [-1, 1] then for every f∈ C[-1, 1] and c > 0 there exists a sequence of polynomials ϕ n of degree ≤ n(l+c) (n ∈ N) which interpolates f at the points X n and it tends to f uniformly in [-1, 1]. The weighted versions of this result were proved in [19] and [18] using Freud-type weights and exponential weights on [-1, 1]. The aim of this paper is to show that analogue statements are true for weighted interpolation if we consider Erdös-type and some ultraspherical weights.