Approximation of integrable functions by general linear operators of their Fourier series at the Lebesgue points

Pointwise estimates of the deviation Tn,A,Bf(⋅)−f(⋅) in terms of moduli of continuity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\bar{w}_{\cdot}f$ \end{document} and w⋅f are proved. Analog results on norm approximation with remarks and corollaries are also given. In the results essentially weaker conditions than those in [2, Theorem 1, p. 437] are used.