The Generalized Non-absolute type of sequence spaces

• Main Authors: Nagarajan Subramanian, M. R. Bivin, Nallaswamy Saivaraju
• Format: Article
• Language: English
• Published: Sociedade Brasileira de Matemática 2016-09-01
• Series: Boletim da Sociedade Paranaense de Matemática
• Subjects: analytic sequence; double sequences; $\chi^{2}$ space; difference sequence space; Musielak - modulus function; $p-$ metric space, Ideal; ideal convergent; fuzzy number; multiplier space; non-absolute type
• Online Access: http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/25674

In this paper we introduce the notion of $\lambda_{mn}-\chi^{2}$ and $\Lambda^{2}$ sequences. Further, we introduce the spaces $\left[\chi^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)}$ and $\left[\Lambda^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)},$ which are of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces $\chi^{2}$ and $\Lambda^{2},$ respectively. Moreover, we establish some inclusion relations between these spaces.