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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Main Authors: Huseyin Cakalli, Mehmet Albayrak
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2014/398379
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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
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issn 2356-6140
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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