New Type Continuities via Abel Convergence
We investigate the concept of Abel continuity. A function f defined on a subset of ℝ, the set of real numbers, is Abel continuous if it preserves Abel convergent sequences. Some other types of continuities are also studied and interesting result is obtained. It turned out that uniform limit of a seq...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/398379 |
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| _version_ | 1850107025197891584 |
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| author | Huseyin Cakalli Mehmet Albayrak |
| author_facet | Huseyin Cakalli Mehmet Albayrak |
| author_sort | Huseyin Cakalli |
| collection | DOAJ |
| description | We investigate the concept of Abel continuity. A function f defined on a subset of ℝ, the set of real numbers, is Abel continuous if it preserves Abel convergent sequences. Some other types of continuities are also studied and interesting result is obtained. It turned out that uniform limit of a sequence of Abel continuous functions is Abel continuous and the set of Abel continuous functions is a closed subset of continuous functions. |
| format | Article |
| id | doaj-art-4bbb207731d647d0975c78efe5f94973 |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-4bbb207731d647d0975c78efe5f949732025-08-20T02:38:41ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/398379398379New Type Continuities via Abel ConvergenceHuseyin Cakalli0Mehmet Albayrak1Department of Mathematics, Maltepe University, Marmara Eğıtım Köyü, Maltepe, 34857 İstanbul, TurkeyDepartment of Mathematics, Sakarya University, Sakarya, 54050 İstanbul, TurkeyWe investigate the concept of Abel continuity. A function f defined on a subset of ℝ, the set of real numbers, is Abel continuous if it preserves Abel convergent sequences. Some other types of continuities are also studied and interesting result is obtained. It turned out that uniform limit of a sequence of Abel continuous functions is Abel continuous and the set of Abel continuous functions is a closed subset of continuous functions.http://dx.doi.org/10.1155/2014/398379 |
| spellingShingle | Huseyin Cakalli Mehmet Albayrak New Type Continuities via Abel Convergence The Scientific World Journal |
| title | New Type Continuities via Abel Convergence |
| title_full | New Type Continuities via Abel Convergence |
| title_fullStr | New Type Continuities via Abel Convergence |
| title_full_unstemmed | New Type Continuities via Abel Convergence |
| title_short | New Type Continuities via Abel Convergence |
| title_sort | new type continuities via abel convergence |
| url | http://dx.doi.org/10.1155/2014/398379 |
| work_keys_str_mv | AT huseyincakalli newtypecontinuitiesviaabelconvergence AT mehmetalbayrak newtypecontinuitiesviaabelconvergence |