Boletim da Sociedade Paranaense de Matemática (Oct 2017)
On multiplicative difference sequence spaces and related dual properties
Abstract
The main purpose of the present article is to introduce the multiplicative difference sequence spaces of order $m$ by defining the multiplicative difference operator $\Delta_{*}^m(x_k)=x^{}_k~x^{-m}_{k+1}~x^{\binom{m}{2}}_{k+2}~x^{-\binom{m}{3}}_{k+3}~x^{\binom{m}{4}}_{k+4}\dots x^{(-1)^m}_{k+m}$ for all $m, k \in \mathbb N$. By using the concept of multiplicative linearity various topological properties are investigated and the relations related to their dual spaces are studied via multiplicative infinite matrices.
Keywords