Fractional ordered Euler Riesz sequence space

Abstract

The main objective of this article is to introduce Euler-Riesz difference sequence spaces of fractional order $\ddot{I}„$ along with infinite matrices. Some topological properties of these spaces are considered here along with the Schauder basis, $\hat{I}\pm -,{\hat{I}}^2-$ and ${\hat{I}}^3-$duals of the spaces. Keywords: Euler-Riesz difference sequence space, difference operator $\left(\hat{I}{”}^{\ddot{I}}„\right)$, Schauder basis, infinite matrices and $\hat{I}\pm -,{\hat{I}}^2-$ and ${\hat{I}}^3-$duals .

15 pages