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

Abstract

The pointwise estimates of the deviations $\widetilde{T}_{n,A,B}^{\text{}%}f\left(\cdot \right) -\widetilde{f}(\cdot)$ and $\widetilde{T}_{n,A,B}^{% \text{}}f\left(\cdot \right) -\widetilde{f}(\cdot,\varepsilon)$ in terms of moduli of continuity $\widetilde{\bar{w}}_{\cdot}f$ and $\widetilde{w}%_{\cdot}f$ are proved. Analogical results on norm approximation with remarks and corollary are also given. These results generalized a theorem of Mittal.