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