On the paranormed Nörlund sequence space of nonabsolute type
type: Item
instance of: scholarly article
title: On the paranormed Nörlund sequence space of nonabsolute type
zbMATH Open document ID: 1468.46014
DOI: 10.1155/2014/858704
author: Medine Yeşilkayagil
author: Feyzi Başar
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: \textit{I. J. Maddox} [Q. J. Math., Oxf. II. Ser. 18, 345--355 (1967; Zbl 0156.06602)] defined the space \(\ell(p)\) of the sequences \(x = (x_k)\) such that \(\sum_{k = 0}^{\infty} | x_k |^{p_k} < \infty\). 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.
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 7023210
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/858704
OpenAlex ID: W2068302823
Wikidata QID: Q59042100
cites work: SPACES OF STRONGLY SUMMABLE SEQUENCES
cites work: Modulared sequence spaces
cites work: The Sequence Spaces l (pv ) and m (pv )
cites work: Lectures on summability
cites work: The inverse Nörlund mean
cites work: On Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations
cites work: Q4693254
cites work: On the paranormed Riesz sequence spaces of non-absolute type
cites work: Q3050957
cites work: Matrix transformations between the sequence spaces of Maddox
cites work: Q5588841
cites work: Q4338822
cites work: Some geometric properties of the domain of the double sequential band matrix \(B(\tilde{r}, \tilde{s})\) in the sequence space \(\ell(p)\)
description: scientific article; zbMATH DE number 7023210