A new series space |N_{p}^{θ}|(μ) and matrix operators with applications

Abstract

The space |N_{p}^{θ}|_{k} of all series summable absolute weighted mean method has recently been introduced and studied by (Sarıgöl 2011), (Sarıgöl 2016) and (Mohapatra and Sarıgöl). In the present paper, we define a new notion of generalized absolute summability method, which includes almost known summabilities, and consruct a series space |N_{p}^{θ}|(μ) corresponding to it. Further, we show that it is a BK-space with AK and characterize certain matrix transformations on that space, and so also deduce some important results as special cases.