Let \(w(x):=w^{(\alpha,\beta)}(x)=(1-x)^ \alpha (1+x)^ \beta\) and let \[ x:\;-1\leq x_ n0.\tag{2} \] \textit{A. Bellen} [J. Approximation Theory 33, 85-95 (1982; Zbl 0484.41003)] raised the following problem: Find a matrix \(Y\) of additional nodes \(Y\): \(-1\leq y_{m(n)}0\), such that \(L_{n+m(n)}(f,x):=L_{n+m(n)}(f,X\cup Y,x)\) satisfies the relation \[ \lim_{n\to\infty} \int_{-1}^ 1 w(x)[L_{n+m(n)}(f;x)-f(x)]^ 2 dx=0\tag{3} \] for some class of functions \(f\) on \([-1,1]\). He showed that if \(X\) consists of zeros of \((1-x^ 2)U_{n-1}(x)\) and \(Y\) is formed by zeros of \(T_ n(x)\), then (3) holds with \(w(x)={1\over{\sqrt{1-x^ 2}}}\) when \(f\in\text{Lip }\gamma\), \(\gamma>{1\over 2}\). Here the author improves this result in an elegant way by showing that if \(f\in C[-1,1]\), then \[ \lim_{n\to\infty} \int_{-1}^ 1 {1\over {\sqrt{1-x^ 2}}}:\;| L_{2n+1}(f;x)- f(x)|^ p dx=0, \qquad p>0.\tag{4} \] .