Integrated and Differentiated Sequence Spaces and Weighted Mean

TL;DR

This paper introduces new sequence spaces via matrix domains, investigates their properties, duals, and transformations, and provides examples relating them to classical and matrix-derived sequence spaces.

Contribution

It constructs novel matrix domains, analyzes their properties, dual spaces, and transformations, and offers illustrative examples connecting them to existing sequence spaces.

Findings

New matrix domains are constructed and their properties are studied.

Dual spaces of the new matrix domains are explicitly computed.

Examples demonstrate relationships between new spaces, classical spaces, and matrix-derived spaces.

Abstract

The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix transformations are characterized. Secondly, examples between new spaces with classical sequence spaces and sequence spaces which are derived by an infinite matrix are given in the table form.