A paranormed fractional ordered Euler-Riesz difference sequence space

Abstract

In this study, we introduce a novel sequence space denoted as & ell;((tau))(p) with a fractional order tau. This new space is defined by the matrix B-similar to(Delta((tau))), which is a composition of the Euler-Riesz matrix B-similar to and the fractional ordered difference operator Delta((tau)). We explore its topological properties along with its alpha-, beta-, and gamma-duals. Furthermore, we provide characterizations for certain matrix mappings from & ell;((tau))(p) to the sequence spaces of Maddox.