$q$-Schr\"{o}der Sequence Spaces and Schr\"{o}der Core

Abstract

This research employs the $q$-Schr\"{o}der matrix $\widetilde{S}_q$ to create the sequence spaces $c_{0}(\widetilde{S}_q)$, $c(\widetilde{S}_q)$, $\ell_{\infty}(\widetilde{S}_q)$ and $\ell_{p}(\widetilde{S}_q)$ where $(1\leqslant p<\infty)$. We demonstrate certain topological features, derive Schauder bases, calculate the alpha, beta, and gamma duals of new sequence spaces, build some matrice classes, and finally show some topological properties. In addition, we give Schr\"{o}der's core of complexly valued sequences and define various inclusion theorems for the new core type.