On double summability methods $\\left| \\mathcal{A}_{f}\\right| _{k}$ and $\\left| C,0,0\\right|_{s}$

Authors : Fadime Gökçe

Pages : 182-189

Doi:10.54187/jnrs.1172611

View : 18 | Download : 6

Publication Date : 2022-12-31

Article Type : Research

Abstract :Recently, for single series, the necessary and sufficient conditions for $\\left\\vert C,0\\right\\vert\\Rightarrow \\left\\vert A_{f}\\right\\vert_{k}$ and vise versa, and $\\left\\vert A_{f}\\right\\vert \\Rightarrow \\left\\vert C,0\\right\\vert_{k}$ and vise versa have been established, where $1 < k < \\infty $ and $A$ is a factorable matrix. The present study extends these results to double summability, and also provides some new results.
Keywords : Double series, Factorable matrix, Absolute Ces$\\grave{a}$ro summability