A new series space |N_p^? |(µ) and matrix operators with applications

Abstract

The space |N_p^? |(µ) all series summable by the absolute weighted mean method has recently been introduced and studied in several publications. In the present paper, we define a new notion of generalized absolute summability, which includes several well-known summability methods, and construct a series space |N_p^? |(µ) corresponding to it. Further, we obtain several properties of the new space and characterize certain matrix transformations on that space. We also deduce some important results as special cases.