A Study on -Quasi-Cauchy Sequences

A Study on -Quasi-Cauchy Sequences

Recently, the concept of -ward continuity was introduced and studied. In this paper, we prove that the uniform limit of -ward continuous functions is -ward continuous, and the set of all -ward continuous functions is a closed subset of the set of all continuous functions. We also obtain that a real...

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Main Authors: Hüseyin Çakalli, Huseyin Kaplan
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/836970
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spelling doaj-93bbfc4d2bdd44269e2d4e479cf111e22020-11-24T21:00:20ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/836970836970A Study on -Quasi-Cauchy SequencesHüseyin Çakalli0Huseyin Kaplan1Maltepe University, Department of Mathematics, Faculty of Arts and Science, Marmara Eğitim Köyü, Maltepe, 34857 Istanbul, TurkeyDepartment of Mathematics, Niğde University, Faculty of Science and Letters, 051100 Niğde, TurkeyRecently, the concept of -ward continuity was introduced and studied. In this paper, we prove that the uniform limit of -ward continuous functions is -ward continuous, and the set of all -ward continuous functions is a closed subset of the set of all continuous functions. We also obtain that a real function defined on an interval is uniformly continuous if and only if (()) is -quasi-Cauchy whenever () is a quasi-Cauchy sequence of points in .http://dx.doi.org/10.1155/2013/836970
collection DOAJ
language English
format Article
sources DOAJ
author Hüseyin Çakalli
Huseyin Kaplan
spellingShingle Hüseyin Çakalli
Huseyin Kaplan
A Study on -Quasi-Cauchy Sequences
Abstract and Applied Analysis
author_facet Hüseyin Çakalli
Huseyin Kaplan
author_sort Hüseyin Çakalli
title A Study on -Quasi-Cauchy Sequences
title_short A Study on -Quasi-Cauchy Sequences
title_full A Study on -Quasi-Cauchy Sequences
title_fullStr A Study on -Quasi-Cauchy Sequences
title_full_unstemmed A Study on -Quasi-Cauchy Sequences
title_sort study on -quasi-cauchy sequences
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description Recently, the concept of -ward continuity was introduced and studied. In this paper, we prove that the uniform limit of -ward continuous functions is -ward continuous, and the set of all -ward continuous functions is a closed subset of the set of all continuous functions. We also obtain that a real function defined on an interval is uniformly continuous if and only if (()) is -quasi-Cauchy whenever () is a quasi-Cauchy sequence of points in .
url http://dx.doi.org/10.1155/2013/836970
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AT huseyinkaplan astudyonquasicauchysequences
AT huseyincakalli studyonquasicauchysequences
AT huseyinkaplan studyonquasicauchysequences
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