Completeness of Sequence Spaces Generated by an Orlicz Function

Nur Khusnussaadah, S. Supama


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.


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

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Eksakta: Journal of Sciences and Data Analysis

E-ISSN 2720-9326 and P-ISSN 2716-0459
Published by: 
Faculty of Mathematics and Natural Sciences
Universitas Islam Indonesia, Yogyakarta

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