A new series space vertical bar(N)over-bar(p)(theta)vertical bar (mu) and matrix operators with applications

Abstract

The space vertical bar(N) over bar (theta)(p)vertical bar 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 vertical bar(N) over bar (theta)(p)vertical bar (mu) 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.