It is shown that best approximation by trigonometric polynomials is achieved in average by families of linear polynomial operators in the -metric for all . This is compared with approximation by Fourier means and interpolation means which is restricted to and , respectively.
Cite this article
Z. Burinska, Konstantin V. Runovski, Hans-Jürgen Schmeisser, On the Method of Approximation by Families of Linear Polynomial Operators. Z. Anal. Anwend. 19 (2000), no. 3, pp. 677–693