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

The goal of this research is to construct the extended versions of the original Maddox’s paranormed sequence spaces, denoted by the notation ℓ(∇2 q, p) and ℓ∞(∇2 q, p). These spaces are linear isomorphic to the spaces ℓ(p) and ℓ∞(p), respectively. The next step is to build the Schauder basis for the ℓ(∇2 q, p) space. After that, the topological features of the alpha, beta, and gamma duals of ℓ(∇2 q, p) and ℓ∞(∇2 q, p) are investigated. Finally, some matrix classes are characterized.