# On sequence spaces generated by binomial difference operator of fractional order

In: Mathematica Slovaca, vol. 69, no. 4
Taja Yaying - Bipan Hazarika
Detaily:
Rok, strany: 2019, 901 - 918
O článku:
In this article we introduce binomial difference sequence spaces of fractional order $α,$ $bpr,s( Δ(α))$ $(1≤ p≤ ∞)$ by the composition of binomial matrix, $Br,s$ and fractional difference operator $Δ(α),$ defined by $\big(Δ(α)x\big)k=∑\limitsi=0(-1)i((Γ(α+1)) / (i!Γ(α-i+1)))xk-i.$ We give some topological properties, obtain the Schauder basis and determine the $α,$ $β$ and $γ$-duals of the spaces. We characterize the matrix classes $(bpr,s(α)),Y),$ where $Y\in\{\ell,c,c0,\ell1 \}$ and certain classes of compact operators on the space $bpr,s(α))$ using Hausdorff measure of non-compactness. Finally, we give some geometric properties of the space $bpr,s(α))$ \$(1
Ako citovať:
ISO 690:
Yaying, T., Hazarika, B. 2019. On sequence spaces generated by binomial difference operator of fractional order. In Mathematica Slovaca, vol. 69, no.4, pp. 901-918. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0276

APA:
Yaying, T., Hazarika, B. (2019). On sequence spaces generated by binomial difference operator of fractional order. Mathematica Slovaca, 69(4), 901-918. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0276
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 19. 7. 2019