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

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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.