Generalization of the space [Formula: see text] derived by absolute Euler summability and matrix operators

The sequence space [Formula: see text] having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345–355, 1967). In the present paper, we generalize the space [Formula: see text] to the space [Formula: see text] derived by the absolute summability of Euler mean...

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Autores principales: Gökçe, Fadime, Sarıgöl, Mehmet Ali
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6004023/
https://www.ncbi.nlm.nih.gov/pubmed/29973772
http://dx.doi.org/10.1186/s13660-018-1724-9
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author Gökçe, Fadime
Sarıgöl, Mehmet Ali
author_facet Gökçe, Fadime
Sarıgöl, Mehmet Ali
author_sort Gökçe, Fadime
collection PubMed
description The sequence space [Formula: see text] having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345–355, 1967). In the present paper, we generalize the space [Formula: see text] to the space [Formula: see text] derived by the absolute summability of Euler mean. Also, we show that it is a paranormed space and linearly isomorphic to [Formula: see text] . Further, we determine α-, β-, and γ-duals of this space and construct its Schauder basis. Also, we characterize certain matrix operators on the space.
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spelling pubmed-60040232018-07-02 Generalization of the space [Formula: see text] derived by absolute Euler summability and matrix operators Gökçe, Fadime Sarıgöl, Mehmet Ali J Inequal Appl Research The sequence space [Formula: see text] having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345–355, 1967). In the present paper, we generalize the space [Formula: see text] to the space [Formula: see text] derived by the absolute summability of Euler mean. Also, we show that it is a paranormed space and linearly isomorphic to [Formula: see text] . Further, we determine α-, β-, and γ-duals of this space and construct its Schauder basis. Also, we characterize certain matrix operators on the space. Springer International Publishing 2018-06-15 2018 /pmc/articles/PMC6004023/ /pubmed/29973772 http://dx.doi.org/10.1186/s13660-018-1724-9 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Gökçe, Fadime
Sarıgöl, Mehmet Ali
Generalization of the space [Formula: see text] derived by absolute Euler summability and matrix operators
title Generalization of the space [Formula: see text] derived by absolute Euler summability and matrix operators
title_full Generalization of the space [Formula: see text] derived by absolute Euler summability and matrix operators
title_fullStr Generalization of the space [Formula: see text] derived by absolute Euler summability and matrix operators
title_full_unstemmed Generalization of the space [Formula: see text] derived by absolute Euler summability and matrix operators
title_short Generalization of the space [Formula: see text] derived by absolute Euler summability and matrix operators
title_sort generalization of the space [formula: see text] derived by absolute euler summability and matrix operators
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6004023/
https://www.ncbi.nlm.nih.gov/pubmed/29973772
http://dx.doi.org/10.1186/s13660-018-1724-9
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AT sarıgolmehmetali generalizationofthespaceformulaseetextderivedbyabsoluteeulersummabilityandmatrixoperators

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