Completeness of Sequence Spaces Generated by an Orlicz Function

Nur Khusnussaadah, S. Supama

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.

Keywords

Convergence Sequence; Orlicz Function; Sequence Space; Orlicz Sequence Space

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References

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Eksakta: Jurnal Ilmu-Ilmu MIPA
Journal of Mathematics and Natural Sciences

ISSN 1411-1047 (print), ISSN 2503-2364 (online)
Published by: 
Faculty of Mathematics and Natural Sciences
Universitas Islam Indonesia, Yogyakarta

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