On Absolute Summability of Factored Infinite Series and Trigonometric Fourier Series

In this paper, a known result dealing with |N¯,pn;θn|k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|\bar{N},p_{n};\theta _{n}|_{k}$$\end{document} summability factors of infinite series, has been proved under weaker conditions. And then this result has been applied to the trigonometric Fourier series. Some new results have also been obtained.