Some New Paranormed Sequence Spaces Derived by $q$-Second Difference Matrix

Abstract

The goal of this research is to construct the extended versions of the originalMaddox's paranormed sequence spaces, denoted by the notation $\ell(\nabla_q^2, p)$and $\ell_\infty(\nabla_q^2, p)$. These spaces are linear isomorphic to the spaces$\ell(p)$ and $\ell_\infty(p)$, respectively. The next step is to build the Schauder basisfor the $\ell(\nabla_q^2, p)$ space. After that, the topological features of the alpha, beta, and gammaduals of $\ell(\nabla_q^2, p)$ and $\ell_\infty(\nabla_q^2, p)$ are investigated. Finally, some matrix classes are characterized.