Upward and Downward Statistical Continuities

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dc.authorid0000-0001-7344-5826en_US
dc.contributor.authorCakalli, Huseyin
dc.date.accessioned2024-07-12T21:47:02Z
dc.date.available2024-07-12T21:47:02Z
dc.date.issued2015en_US
dc.departmentMaltepe Üniversitesien_US
dc.description.abstractA real valued function f defined on a subset E of R, the set of real numbers, is statistically upward (resp. downward) continuous if it preserves statistically upward (resp. downward) half quasi-Cauchy sequences; A subset E of R, is statistically upward (resp. downward) compact if any sequence of points in E has a statistically upward (resp. downward) half quasi-Cauchy subsequence, where a sequence (x(n)) of points in R is called statistically upward half quasi-Cauchy if lim(n ->infinity) 1/n vertical bar{k <= n : x(k) - x(k+1) >= epsilon}vertical bar = 0 and statistically downward half quasi-Cauchy if lim(n ->infinity) 1/n vertical bar{k <= n : x(k+1) - x(k) >= epsilon}vertical bar = 0 for every epsilon > 0. We investigate statistically upward and downward continuity, statistically upward and downward half compactness and prove interesting theorems. It turns out that any statistically upward continuous function on a below bounded subset of R is uniformly continuous, and any statistically downward continuous function on an above bounded subset of R is uniformly continuous.en_US
dc.identifier.doi10.2298/FIL1510265C
dc.identifier.endpage2273en_US
dc.identifier.issn0354-5180
dc.identifier.issue10en_US
dc.identifier.scopus2-s2.0-84949438862en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage2265en_US
dc.identifier.urihttps://dx.doi.org/10.2298/FIL1510265C
dc.identifier.urihttps://hdl.handle.net/20.500.12415/7995
dc.identifier.volume29en_US
dc.identifier.wosWOS:000366736800010en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorCakalli, Huseyin
dc.language.isoenen_US
dc.publisherUNIV NIS, FAC SCI MATHen_US
dc.relation.ispartofFILOMATen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmzKY01038
dc.subjectcontinuityen_US
dc.subjectcompactnessen_US
dc.subjectsequencesen_US
dc.subjectsummabilityen_US
dc.titleUpward and Downward Statistical Continuitiesen_US
dc.typeArticle
dspace.entity.typePublication

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