On Generalized p , q -Euler Matrix and Associated Sequence Spaces

Abstract

In this study, we introduce new $\text{BK}$ -spaces $b_s^{r,t}\left(p,q\right)$ and $b_{\infty }^{r,t}\left(p,q\right)$ derived by the domain of $\left(p,q\right)$ -analogue $B^{r,t}\left(p,q\right)$ of the binomial matrix in the spaces ${\ell }_s$ and ${\ell }_{\infty },$ respectively. We study certain topological properties and inclusion relations of these spaces. We obtain a basis for the space $b_s^{r,t}\left(p,q\right)$ and obtain Köthe-Toeplitz duals of the spaces $b_s^{r,t}\left(p,q\right)$ and $b_{\infty }^{r,t}\left(p,q\right).$ We characterize certain classes of matrix mappings from the spaces $b_s^{r,t}\left(p,q\right)$ and $b_{\infty }^{r,t}\left(p,q\right)$ to space $\mu \in \left\{{\ell }_{\infty },c,c_0,{\ell }_1,bs,cs,c{s}_0\right\}.$ Finally, we investigate certain geometric properties of the space $b_s^{r,t}\left(p,q\right).$