On best one-sided approximation by spline polynomials in weighted space Lp,w(X)

Abstract

Positive results for spline approximation in weighted space L p,w (X), (1 ≤ p < ∞) are obtained. In particular its show that the degree of best one-sided approximation in terms the k th local modulus of L p,w-continuity and Ditzian-Totic modulus of smoothness for f ∈ L p,w (X).