Geodesic
Paranormed Riesz Difference Sequence Spaces of Fractional Order
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 2, p. 175
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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.
Classification : 46A45 46A35, 46B45
Keywords: Riesz difference sequence spaces, difference operator $\Delta^{(\alpha)}$, Schauder basis, $\alpha$-, $\beta$-, $\gamma$- duals, matrix transformation 
@article{KJM_2022_46_2_a0,
     author = {Taja Yaying},
     title = {Paranormed {Riesz} {Difference} {Sequence} {Spaces} of {Fractional} {Order}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {175 },
     year = {2022},
     volume = {46},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_2_a0/}
}
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Taja Yaying. Paranormed Riesz Difference Sequence Spaces of Fractional Order. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 2, p. 175 . http://geodesic.mathdoc.fr/item/KJM_2022_46_2_a0/