The Generalized Non-absolute type of sequence spaces

Nagarajan Subramanian; M. R. Bivin; Nallaswamy Saivaraju

doi:10.5269/bspm.v34i1.25674

Nagarajan Subramanian SASTRA University https://orcid.org/0000-0002-5895-673X
M. R. Bivin Care Group of Institutions
Nallaswamy Saivaraju Sri Angalamman College of Engineering and Technology

DOI: https://doi.org/10.5269/bspm.v34i1.25674

Keywords: 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

Abstract

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.

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Author Biographies

Nagarajan Subramanian, SASTRA University

Department of Mathematics

M. R. Bivin, Care Group of Institutions

Department of Mathematics

Nallaswamy Saivaraju, Sri Angalamman College of Engineering and Technology

Department of Mathematics

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