On paranorm BVσ I-convergent double sequence spaces defined by an Orlicz function
Abstract The space BV σ {\mathrm{BV}_{\sigma}} was introduced and studied by Mursaleen [21]. In the present article we study the double sequence spaces ( 0 BV ( M , p ) σ I ) 2 {{}_{2}(_{0}\mathrm{BV}{{}^{I}_{\sigma}}(M,p))} , BV 2 ( M , p ) σ I {{}_{2}\mathrm{BV}{{}^{I}_{\sigma}}(M,p)} and ( ∞ BV ( M , p ) σ I ) 2 {{}_{2}(_{\infty}\mathrm{BV}{{}^{I}_{\sigma}}(M,p))} with the help of the space BV σ {\mathrm{BV}_{\sigma}} and an Orlicz function M, where p = ( p i ⁢ j ) {p=(p_{ij})} is the double sequence of strictly positive real numbers. We study some of its properties and prove some inclusion relations related to these new spaces.