On non-absolute type spaces and their Köthe-Toeplitz duals

In this paper, we introduce and study some non-absolute type spaces $l_{\infty }(u,\lambda ,{\Delta }_v^m)$, $c_0(u,\lambda ,{\Delta }_v^m)$ and $c(u,\lambda ,{\Delta }_v^m)$, which are $\mathrm{BK}$-spaces. Moreover, we prove that these spaces are linearly isomorphic to the spaces $l_{\infty },c_0$ and $c$. We also make an effort to establish some inclusion relations between these spaces. Furthermore, we find the Schauder basis for these spaces and also determine the $\alpha$-, $\beta$- and $\gamma$-duals of these spaces.