Completeness of Sequence Spaces Generated by an Orlicz Function

Eksakta: Jurnal Ilmu-Ilmu MIPA

Nur Khusnussaadah¹  S. Supama¹ 

[1] Departemen Matematika FMIPA UGM, Yogyakarta;

关键词: Convergence Sequence;    Orlicz Function;    Sequence Space;    Orlicz Sequence Space;   

DOI  :  10.20885/eksakta.vol19.iss1.art1

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown