Completeness of Sequence Spaces Generated by an Orlicz Function - Nur Khusnussaadah; S. Supama (EKSAKTA: Journal of Sciences and Data Analysis, 2019)
In this paper, we discuss about completeness property of Orlicz sequence spaces defined by an Orlicz function. Orlicz sequence space is generalization of p-summable sequence space, for every which is also an Orlicz sequence space. Based on the property of convergence sequence on norm space, we define $Φ$-convergence sequence on Orlicz sequence space. Moreover, we define $Φ$-Cauchy sequence and $Φ$-complete on Orlicz sequence space. In this paper, we show the relationship between the (ordinary) convergent sequence, $Φ$-convergent and $Φ$-Cauchy sequences. Finally, it will also be shown that Orlicz sequence space is Banach space and $Φ$-complete space.