TITLE

# A variation on Abel quasi Cauchy sequences

AUTHOR(S)
Çakallı, Hüseyin
PUB. DATE
September 2015
SOURCE
AIP Conference Proceedings;2015, Vol. 1676 Issue 1, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, we introduce and investigate the concept of Abel ward continuity. A real function Âƒ is Abel ward continuous if it preserves Abel quasi Cauchy sequences, where a sequence (pk) of point in R is called Abel quasi-Cauchy if the series Î£k=0âˆžâ–³pkÂ·xk is convergent for 0 â‰¤ x < 1 and limxâ†’1-(1-x)Î£k=0âˆžâ–³pkÂ·xk=0, where â†’ pk = pk+1 - pk for every non negative integer k. Some other types of continuities are also studied and interesting results are obtained. It turns out that uniform limit of a sequence of Abel ward continuous functions is Abel ward continuous and the set of Abel ward continuous functions is a closed subset of the set of continuous functions.
ACCESSION #
109578203

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