Approximation of integrable functions by general linear matrix operators of their Fourier series

Abstract

The pointwise estimates of the deviation Tn,Af(⋅)−f(⋅){T}_{n,A}f(\cdot )-f\left(\cdot ) in terms of pointwise moduli of continuity based on the points of differentiability of indefinite integral of ff, with application of the rth differences of the entries of AA, are proved. The similar results in case of the Lebesgue points are considered, too. Analogical results on norm approximation with remarks and corollaries are also given.

Keywords

• rate of approximation
• summability of fourier series
• 42a24