Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces

We define the notions of double statistically convergent and double lacunary statistically convergent sequences in locally solid Riesz space and establish some inclusion relations between them. We also prove an extension of a decomposition theorem in this setup. Further, we introduce the concepts of...

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Main Authors:	S. A. Mohiuddine, Bipan Hazarika, Abdullah Alotaibi
Format:	Article
Language:	English
Published:	Hindawi Limited 2013-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2013/507962

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spelling	doaj-10db540cf5fc4a30a5d27cdbe52fd6fa2020-11-24T21:47:29ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/507962507962Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz SpacesS. A. Mohiuddine0Bipan Hazarika1Abdullah Alotaibi2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh 791 112, IndiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe define the notions of double statistically convergent and double lacunary statistically convergent sequences in locally solid Riesz space and establish some inclusion relations between them. We also prove an extension of a decomposition theorem in this setup. Further, we introduce the concepts of double θ-summable and double statistically lacunary summable in locally solid Riesz space and establish a relationship between these notions.http://dx.doi.org/10.1155/2013/507962
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	S. A. Mohiuddine Bipan Hazarika Abdullah Alotaibi
spellingShingle	S. A. Mohiuddine Bipan Hazarika Abdullah Alotaibi Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces Abstract and Applied Analysis
author_facet	S. A. Mohiuddine Bipan Hazarika Abdullah Alotaibi
author_sort	S. A. Mohiuddine
title	Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces
title_short	Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces
title_full	Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces
title_fullStr	Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces
title_full_unstemmed	Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces
title_sort	double lacunary density and some inclusion results in locally solid riesz spaces
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2013-01-01
description	We define the notions of double statistically convergent and double lacunary statistically convergent sequences in locally solid Riesz space and establish some inclusion relations between them. We also prove an extension of a decomposition theorem in this setup. Further, we introduce the concepts of double θ-summable and double statistically lacunary summable in locally solid Riesz space and establish a relationship between these notions.
url	http://dx.doi.org/10.1155/2013/507962
work_keys_str_mv	AT samohiuddine doublelacunarydensityandsomeinclusionresultsinlocallysolidrieszspaces AT bipanhazarika doublelacunarydensityandsomeinclusionresultsinlocallysolidrieszspaces AT abdullahalotaibi doublelacunarydensityandsomeinclusionresultsinlocallysolidrieszspaces
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Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces

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