The modular sequence space of $\chi^{2}$

Abstract

In this paper we introduce the modular sequence space of $\chi^{2}$ and examine some topological properties of these space also establish some duals results among them. Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space $\ell_{M}$ which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. We define the sequence spaces $\chi^{2}_{f\lambda}$ and $\chi^{2\lambda}_{g},$ where $f=\left(f_{mn}\right)$ and $g=\left(g_{mn}\right)$ are sequences of modulus functions such that $f_{mn}$ and $g_{mn}$ be mutually complementary for each $m,n.$