On Generalized Local Property of $|A;\delta|_{k}$-Summability of Factored Fourier Series

Abstract

The convergence of Fourier series of a function at a point depends upon the behaviour of the function in the neighborhood of that point and it leads to the local property of Fourier series. In the proposed paper a new result on local property of $|\mathcal{A};\delta|_{k}$-summability of factored Fourier series has been established that generalizes a theorem of Sarig\"{o}l [13] (see [M. A. Sari\"{o}gol, On local property of $|\mathcal{A}|_{k}$-summability of factored Fourier series, \textit{J. Math. Anal. Appl.} 188 (1994), 118-127]) on local property of $|\mathcal{A}|_{k}$-summability of factored Fourier series.