On generalized \((p,q)\)-Euler matrix and associated sequence spaces (Q2046619)

Summary: In this study, we introduce new \(\mathrm{BK} \)-spaces \(b_{s}^{r,t}(p,q)\) and \(b_{\infty}^{r,t}(p,q)\) derived by the domain of \((p,q)\)-analogue \(B^{r,t}(p,q)\) 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 \(b_{s}^{r,t}(p,q)\) and obtain Köthe-Toeplitz duals of the spaces \(b_{s}^{r,t}(p,q)\) and \(b_{\infty}^{r,t}(p,q)\). We characterize certain classes of matrix mappings from the spaces \(b_{s}^{r,t}(p,q)\) and \(b_{\infty}^{r,t}(p,q)\) to space \(\mu\in\{\ell_{\infty}, c, c_{0}, \ell_{1}, bs, cs, cs_{0}\}\). Finally, we investigate certain geometric properties of the space \(b_{s}^{r,t}(p,q)\).