Fractional ordered Euler Riesz sequence space

TL;DR

This paper introduces fractional order Euler-Riesz difference sequence spaces, exploring their topological properties, duals, and basis structures, expanding the mathematical framework for fractional difference sequences.

Contribution

It defines and analyzes new fractional order Euler-Riesz sequence spaces, including their topological properties and duals, which were not previously studied.

Findings

Established the topological properties of the new spaces.

Determined the Schauder basis for these spaces.

Computed the α-, β-, and γ-duals of the spaces.

Abstract

The main objective of this article is to introduce Euler-Riesz difference sequence spaces of fractional order ${\tau} $ along with infinite matrices. Some topological properties of these spaces are considered here along with the Schauder basis, ${\alpha} -,\beta -$ and $\gamma -$duals of the spaces. Keywords: Euler-Riesz difference sequence space, difference operator $\left(\Delta ^{\tau} \right)$, Schauder basis, infinite matrices and ${\alpha} -,\beta -$ and $\gamma -$duals .