Binomial difference sequence spaces of fractional order.

Abstract

In this paper, we introduce the sequence spaces $b_0^{r,s}\left({\nabla }^{\left(\alpha \right)}\right)$ , $b_c^{r,s}\left({\nabla }^{\left(\alpha \right)}\right)$ , and $b_{\infty }^{r,s}\left({\nabla }^{\left(\alpha \right)}\right)$ . We investigate some functional properties, inclusion relations, and the α-, β-, γ-, and continuous duals of these sets.