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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/836970 |
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| _version_ | 1832551358974132224 |
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| author | Hüseyin Çakalli Huseyin Kaplan |
| author_facet | Hüseyin Çakalli Huseyin Kaplan |
| author_sort | Hüseyin Çakalli |
| collection | DOAJ |
| 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 . |
| format | Article |
| id | doaj-art-93bbfc4d2bdd44269e2d4e479cf111e2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-93bbfc4d2bdd44269e2d4e479cf111e22025-02-03T06:01:40ZengWileyAbstract 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 |
| spellingShingle | Hüseyin Çakalli Huseyin Kaplan A Study on -Quasi-Cauchy Sequences Abstract and Applied Analysis |
| title | 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_short | A Study on -Quasi-Cauchy Sequences |
| title_sort | study on quasi cauchy sequences |
| url | http://dx.doi.org/10.1155/2013/836970 |
| work_keys_str_mv | AT huseyincakalli astudyonquasicauchysequences AT huseyinkaplan astudyonquasicauchysequences AT huseyincakalli studyonquasicauchysequences AT huseyinkaplan studyonquasicauchysequences |