Paranormed Riesz Difference Sequence Spaces of Fractional Order

Taja Yaying

Kragujevac Journal of Mathematics, Tome 46 (2022) no. 2, p. 175

Résumé

In this article we introduce paranormed Riesz difference sequence spaces of fractional order $\alpha,$ $r_0^t\left(p, \Delta^{(\alpha)}\right),$ $r_c^t\left(p, \Delta^{(\alpha)}\right)$ and $r_{\infty}^t\left(p, \Delta^{(\alpha)}\right) $ defined by the composition of fractional difference operator $\Delta^{(\alpha)},$ defined by $(\Delta^{(\alpha)}x)_k=\sum\limits_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i},$ and Riesz mean matrix $R^t.$ We give some topological properties, obtain the Schauder basis and determine the $\alpha$-, $\beta$- and $\gamma$- duals of the new spaces. Finally, we characterize certain matrix classes related to these new spaces.

Détail

Classification : 46A45 46A35, 46B45
Keywords: Riesz difference sequence spaces, difference operator $\Delta^{(\alpha)}$, Schauder basis, $\alpha$-, $\beta$-, $\gamma$- duals, matrix transformation