Completeness of Sequence Spaces Generated by an Orlicz Function - Nur Khusnussaadah; S. Supama (Fakultas Matematika dan Ilmu Pengetahuan Alam, 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.