The lower estimate for the linear combinations of Bernstein-Kantorovich operators (Q979033)

To improve the error of estimating an \(L_p\) \((1 \leq p < \infty)\) \(f\) by its Bernstein-Kantorovich operator approximation, the authors compute estimates for approximating \(f\) by a linear combination of a fixed number of Bernstein-Kantorovich operator approximates. For example, the paper establishes when the error of \(r\) combinations of Bernstein-Kantorovich operator approximates of degree \(\leq n\) goes to zero like \(n-r\). The estimate involves complicated technical terms.