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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Detalles Bibliográficos
Autores principales: Cakalli, Huseyin, Albayrak, Mehmet
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032686/
https://www.ncbi.nlm.nih.gov/pubmed/24883393
http://dx.doi.org/10.1155/2014/398379
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author Cakalli, Huseyin
Albayrak, Mehmet
author_facet Cakalli, Huseyin
Albayrak, Mehmet
author_sort Cakalli, Huseyin
collection PubMed
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.
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spelling pubmed-40326862014-06-01 New Type Continuities via Abel Convergence Cakalli, Huseyin Albayrak, Mehmet ScientificWorldJournal Research Article 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. Hindawi Publishing Corporation 2014 2014-04-27 /pmc/articles/PMC4032686/ /pubmed/24883393 http://dx.doi.org/10.1155/2014/398379 Text en Copyright © 2014 H. Cakalli and M. Albayrak. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Cakalli, Huseyin
Albayrak, Mehmet
New Type Continuities via Abel Convergence
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
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032686/
https://www.ncbi.nlm.nih.gov/pubmed/24883393
http://dx.doi.org/10.1155/2014/398379
work_keys_str_mv AT cakallihuseyin newtypecontinuitiesviaabelconvergence
AT albayrakmehmet newtypecontinuitiesviaabelconvergence

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