On Modular Difference Sequence Spaces

Parmeshwary Dayal Srivastava, Atanu Manna

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Keywords:

modular sequence spaces, modular spaces, difference sequence, Baire category

Abstract

In this paper, using $m$-th order difference operator $\Delta^{(m)}$ and a sequence $\{\alpha_n\}_{n=0}^{\infty}$ of strictly positive real numbers, sequence spaces $\Delta^{(m)}l_\alpha\{f_n\}=\{x\in s:(\Delta^{(m)}x)_j\in l_\alpha\{f_n\}\}$ and $\Delta^{(m)}l^\alpha\{g_n\} = \{x\in s :(\Delta^{(m)}x)_j \in l^{\alpha}\{g_n\}\}$ are introduced, where $x=\{\xi_j\}_{j=0}^{\infty}\in s$ and $ \{f_n\}_{n=0}^{\infty}$, $ \{g_n\}_{n=0}^{\infty}$ are sequence of Orlicz functions. It is shown that these are separable Banach spaces and dense $F_\sigma$-set of the first Baire category in $s$, the space of all real sequences with the Fr\`{e}chet metric. Some earlier results related to Baire category are obtained when the sequence $\{\alpha_n\}_{n=0}^{\infty}$ is chosen specifically.

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Published

2018-12-01

How to Cite

Team, S. (2018). On Modular Difference Sequence Spaces: Parmeshwary Dayal Srivastava, Atanu Manna. Thai Journal of Mathematics, 16(3), 757–774. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/829

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