The Estimate of the Degree of Approximation Using an Extended Chebyshev System

Abstract

If ψ₁, ψ₂, ψ₃  is an extended Chebyshev system on the interval [a, b] and L is a positive linear operator on C[a, b], such that L(ψ_i) = ψ_i, i = 1, 2, then one obtains an estimate of the difference L(f, x) – f(x), in terms of certain adapted second order moduli for the given extended Chebychev system.