Second degree Schoenberg operators with knots at the roots of Chebyshev polynomials

Abstract

In this paper, it is shown that Schoenberg spline operators of degree two with the knots at the roots of Chebyshev polynomials have the degree of pointwise approximation of order $$\mathrm{O}\Big (\omega _1\Big (\psi ,\frac{\sqrt{t(1-t)}}{n}\Big )\Big )$$ , $$\psi \in C[0,1]$$ , which improves the order of pointwise approximation obtained by Schoenberg operators with equidistant knots.