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

• Multiplicaitve difference sequence spaces
• multiplicative difference operator $\Delta_m^*$
• multiplicative linear spaces
• $\beta$-duals