On the Paranormed Nörlund Sequence Space of Nonabsolute Type

Medine Yeşilkayagil; Feyzi Başar

doi:10.1155/2014/858704

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2014 On the Paranormed Nörlund Sequence Space of Nonabsolute Type

Medine Yeşilkayagil, Feyzi Başar

Abstr. Appl. Anal. 2014(SI26): 1-9 (2014). DOI: 10.1155/2014/858704

Abstract

Maddox defined the space $\ell (p)$ of the sequences $x=({x}_{k})$ such that ${\sum }_{k=\mathrm{0}}^{\mathrm{\infty }}\mathrm{‍}|{x}_{k}{|}^{{p}_{k}}<\mathrm{\infty }$ , in Maddox, 1967. In the present paper, the Nörlund sequence space ${N}^{t}(p)$ of nonabsolute type is introduced and proved that the spaces ${N}^{t}(p)$ and $\ell (p)$ are linearly isomorphic. Besides this, the alpha-, beta-, and gamma-duals of the space ${N}^{t}(p)$ are computed and the basis of the space ${N}^{t}(p)$ is constructed. The classes $({N}^{t}(p):\mu )$ and $(\mu :{N}^{t}(p))$ of infinite matrices are characterized. Finally, some geometric properties of the space ${N}^{t}(p)$ are investigated.

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Medine Yeşilkayagil. Feyzi Başar. "On the Paranormed Nörlund Sequence Space of Nonabsolute Type." Abstr. Appl. Anal. 2014 (SI26) 1 - 9, 2014. https://doi.org/10.1155/2014/858704