Some Paranormed Sequence Spaces Which Involve Arithmetic Divisor Sum Function

Abstract

Let Dr, r >= 0, be a triangle and q = (qj) be a bounded sequence of strictly positive numbers. In this paper, we study the algebraic and topological properties of the paranormed sequence space & ell;Dr,q, generated by the triangle Dr over Maddox ' s space & ell;(q). We identify the Schauder basis as well as the alpha-, beta-, and gamma-duals of the space & ell;Dr,q. One section is devoted to characterizing matrix classes & ell;Dr,q,X, where X is any of the spaces & ell;infinity, c, and c0, and also presents the characterization of some other matrix classes related to the space & ell;Dr,q as corollaries derived from a main result. The final section explores the geometric properties of the space & ell;Dr,q.