On some properties of new paranormed sequence space of non-absolute type

TL;DR

This paper introduces new generalized sequence spaces related to l(p), explores their topological properties, duals, and matrix transformations, expanding the understanding of paranormed sequence spaces of non-absolute type.

Contribution

It presents novel generalized sequence spaces of non-absolute type, analyzes their topological properties, duals, and matrix transformations, which were not previously studied.

Findings

The new sequence spaces are complete and topologically isomorphic to known spaces.

The alpha-, beta-, and gamma-duals of these spaces are explicitly characterized.

Inclusion relations with other sequence spaces are established.

Abstract

In this work, we introduce some new generalized sequence space related to the space l(p). Furthermore we investigate some topological properties as the completeness, the isomorphism and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute alpha-, beta- and gamma-duals of this space, and characterize certain matrix transformations on this sequence space.