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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/836970 |
| Summary: | 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 . |
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| ISSN: | 1085-3375 1687-0409 |