Yeni $\Delta _{q}^{v}$-fark operatörü ve topolojik özellikleri

Abstract

$\Delta_{q}^{v}$ fark operatörünü kullanarak $\Delta^{v}$’yi genişlettik. $l_{p} (\Delta_{q}^{v} )$ fark dizi uzayını oluşturduk ve bazı topolojik özelliklerini inceledik. Eğer $l_{p} (\Delta_{q}^{v} )$ uygun bir $\left\| . \right\|_{p,\Delta_{q}^{v} } $ normu verilirse bunun bir Banach uzayı olacağını gösterdik. Ayrıca $\left({l_{p} (\Delta_{q}^{v} ),\left\| . \right\|_{p,\Delta_{q}^{v} } } \right)$ ve $\left( {l_{p} ,\left\| . \right\|_{p} } \right)$ dizi uzaylarının lineer izometrik olduklarını gösterdik. Çalışmanın sonunda ise $l_{p}(\Delta _{q}^{v})\subset l_{p}\left( \cal M,\Delta _{q}^{v}\right) $ olduğu gösterildi. Orlicz fonksiyonlarının ailesi ${\cal M}$, $\Delta_{2}$ şartı ile örtüşmektedir.

Keywords

• Fark dizi uzayları
• izometrik dizi uzayları
• dizi uzayları

New $\Delta _{q}^{v}$ -difference operator and topological features

Abstract

We extented $\Delta^{v}$ by using difference operator $\Delta_{q}^{v}$. We generated the difference sequence space $l_{p} (\Delta_{q}^{v} )$ and investigated some of their properties. We showed that, if $l_{p} (\Delta_{q}^{v} )$ is supplied with an proper norm $\left\| . \right\|_{p,\Delta_{q}^{v} } $ then it will be a Banach space. We further more showed that, the sequence spaces $\left({l_{p} (\Delta_{q}^{v} ),\left\| . \right\|_{p,\Delta_{q}^{v} } } \right)$ and $\left( {l_{p} ,\left\| . \right\|_{p} } \right)$ are linearly isometric. At the end of this studies, it was shown that $l_{p}(\Delta _{q}^{v})\subset l_{p}\left( M,\Delta _{q}^{v}\right) $. The family of the Orlicz functions ${\cal M}$ is coincides the $\Delta_{2}$ condition.

Keywords

• Difference sequence spaces
• isometric sequence spaces
• sequence spaces

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