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Nur Khusnussaadah
Departemen Matematika FMIPA UGM, Yogyakarta
Chemical Engineering, Chemistry & Bioengineering Chemistry Earth & Planetary Sciences Materials Science & Nanotechnology

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Completeness of Sequence Spaces Generated by an Orlicz Function Nur Khusnussaadah; S. Supama
EKSAKTA: Journal of Sciences and Data Analysis VOLUME 19, ISSUE 1, February 2019
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20885/eksakta.vol19.iss1.art1

Abstract

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.
Co-Authors S. Supama