In this paper, we introduce two degenerate binomial sequence spaces \(b_{p}^{r,s,\lambda }\) and \(b_{\infty }^{r,s,\lambda }\) and show that these are linearly isomorphic to the classical spaces \(\ell _{p}\) and \(\ell _{\infty }\) , respectively. Also, we give the \(\beta \) -duals for both the spaces and we derive the characterization of certain classes of matrix mappings pertaining to the spaces \(b_{p}^{r,s,\lambda }\) and \(b_{\infty }^{r,s,\lambda }\) . Moreover, we deal with the characterization of compact operators acting on the spaces by using Hausdorff measure of non-compactness.
