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.
@article{29182,
title = {On multiplicative difference sequence spaces and related dual properties},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {35},
year = {2016},
doi = {10.5269/bspm.v35i3.29182},
language = {EN},
url = {http://dml.mathdoc.fr/item/29182}
}
Kadak, Ugur. On multiplicative difference sequence spaces and related dual properties. Boletim da Sociedade Paranaense de Matemática, Tome 35 (2016) . doi : 10.5269/bspm.v35i3.29182. http://gdmltest.u-ga.fr/item/29182/