Abstract and Applied Analysis

On the Paranormed Nörlund Sequence Space of Nonabsolute Type

Medine Yeşilkayagil and Feyzi Başar

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Abstract

Maddox defined the space ( p ) of the sequences x = ( x k ) such that k = 0 | x k | p k < , 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 ( 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 ) : μ ) and ( μ : N t ( p ) ) of infinite matrices are characterized. Finally, some geometric properties of the space N t ( p ) are investigated.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 858704, 9 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606524

Digital Object Identifier
doi:10.1155/2014/858704

Mathematical Reviews number (MathSciNet)
MR3191072

Zentralblatt MATH identifier
07023210

Citation

Yeşilkayagil, Medine; Başar, Feyzi. On the Paranormed Nörlund Sequence Space of Nonabsolute Type. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 858704, 9 pages. doi:10.1155/2014/858704. https://projecteuclid.org/euclid.aaa/1412606524


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