On local property of absolute summability of factored Fourier series
Abstract
We establish two general theorems on the local properties of the
absolute summability of factored Fourier series by applying a
recently defined absolute summability, $\left\vert
A,\alpha_{n}\right\vert _{k}$ summability, and the class
$\mathcal{S}\left( \alpha_{n},\phi_{n}\right) $, which generalize some well known results and can be applied to improve many classical absolute summability methods.
absolute summability of factored Fourier series by applying a
recently defined absolute summability, $\left\vert
A,\alpha_{n}\right\vert _{k}$ summability, and the class
$\mathcal{S}\left( \alpha_{n},\phi_{n}\right) $, which generalize some well known results and can be applied to improve many classical absolute summability methods.
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