On double absolute factorable matrix summability

Abstract

In this article a new result on |A, pm, qn; δ| k summability of doubly infinite lower triangular matrix has been establised which generalizes a theorem of E. Savas and B.E. Rhoades and subsequently a theorem of Paikray et al. on summability factor of double infinite weighted mean matrix.

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

“…Also, if we take A = (C, α) with (α > −1), then |A, δ| k -summability becomes |C, α, (α − 1)(1 − 1/k)δ| k in Flett's notation. Furthermore, for double absolute factorable summability matrix (see [11]). …”