Completeness of Sequence Spaces Generated by an Orlicz Function
| Main Authors: | Khusnussaadah, Nur, Supama, S. |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
Fakultas Matematika dan Ilmu Pengetahuan Alam
, 2019
|
| Subjects: | |
| Online Access: |
https://journal.uii.ac.id/Eksakta/article/view/9947 https://journal.uii.ac.id/Eksakta/article/view/9947/pdf |
Daftar Isi:
- 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 $\Phi$-convergence sequence on Orlicz sequence space. Moreover, we define $\Phi$-Cauchy sequence and $\Phi$-complete on Orlicz sequence space. In this paper, we show the relationship between the (ordinary) convergent sequence, $\Phi$-convergent and $\Phi$-Cauchy sequences. Finally, it will also be shown that Orlicz sequence space is Banach space and $\Phi$-complete space.