Fibonomial matrix and its domain in the spaces $\ell_p$ and $\ell_{\infty}$

Authors: MUHAMMET CİHAT DAĞLI, TAJA YAYING

Abstract: In this paper, we introduce the fibonomial sequence spaces $b_{p}^{r,s,F}$ and $b_{\infty}^{r,s,F},$ and show that these are BK-spaces. Also, we prove that these new spaces are linearly isomorphic to $\ell_{p}$ and $\ell_{\infty}.$ Moreover, we determine the $\alpha$-, $\beta$-, $\gamma$-duals for these new spaces and characterize some matrix classes. The final section is devoted to the investigation of some geometric properties of the newly defined space $b_{p}^{r,s,F}.$

Keywords: Fibonomial sequence spaces, Schauder basis, $\alpha$-, $\beta$-, $\gamma$-duals, matrix transformations, geometric properties

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