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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Bibliographic Details
Published in:TheScientificWorld 2014-01, Vol.2014 (2014), p.1-6
Main Authors: Cakalli, Huseyin, Albayrak, Mehmet
Format: Article
Language:English
Subjects:
Continuity
Convergence
Convergence (Mathematics)
Dynamical systems
Information theory
Investigations
Mathematical research
Mathematics
Mathematics - methods
Models, Theoretical
Numbers
Science
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Summary: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.
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2014/398379