On the spaces of Fibonacci difference absolutely $p$-summable, null and convergent sequences

Abstract

Let $0<p<1$. In the present paper, as the domain of the band matrix $\widehat{F}$ defined by the Fibonacci sequence in the classical sequence spaces $\ell_{p}$, $c_{0}$ and $c$, we introduce the sequence spaces $\ell_{p}(\widehat{F})$, $c_{0}(\widehat{F})$ and $c(\widehat {F})$, respectively. Also, we give some inclusion relations and construct the bases of the spaces $c_{0}(\widehat{F})$ and $c(\widehat{F})$. Finally, we compute the alpha, beta, gamma duals of these spaces and characterize the classes $(\ell_{p}(\widehat{F}),\mu)$ of infinite matrices with $\mu\in\{\ell_{\infty},c,c_{0}\}$.