A new series space {equation presented} and matrix operators with applications

Abstract

The space {equation presented} of 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 {equation presented} 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. © 2018 University of Kuwait. All Rights Reserved.