Beyond Cauchy and Quasi-Cauchy Sequences

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dc.authorid0000-0001-7344-5826en_US
dc.contributor.authorCakalli, Huseyin
dc.date.accessioned2024-07-12T21:47:00Z
dc.date.available2024-07-12T21:47:00Z
dc.date.issued2018en_US
dc.departmentMaltepe Üniversitesien_US
dc.description3rd International Conference on Analysis and Applied Mathematics (ICAAM) -- SEP 07-10, 2016 -- Almaty, KAZAKHSTANen_US
dc.description.abstractIn this paper, we investigate the concepts of downward continuity and upward continuity. A real valued function on a subset E of R, the set of real numbers, is downward continuous if it preserves downward quasi-Cauchy sequences; and is upward continuous if it preserves upward quasi-Cauchy sequences, where a sequence (x(k)) of points in R is called downward quasi-Cauchy if for every epsilon > 0 there exists an n(0) is an element of N such that x(n+1) xn < epsilon for n >= n(0), and called upward quasi-Cauchy if for every epsilon > 0 there exists an n(1) is an element of N such that xn x(n+1) < epsilon for n >= n(1). We investigate the notions of downward compactness and upward compactness and prove that downward compactness coincides with above boundedness. It turns out that not only the set of downward continuous functions, but also the set of upward continuous functions is a proper subset of the set of continuous functions.en_US
dc.description.sponsorshipInst Math & Math Modeling, Al Farabi Kazakh Natl Univ, L N Gumilyov Eurasian Natl Univen_US
dc.identifier.doi10.2298/FIL1803035C
dc.identifier.endpage1042en_US
dc.identifier.issn0354-5180
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85048003771en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage1035en_US
dc.identifier.urihttps://dx.doi.org/10.2298/FIL1803035C
dc.identifier.urihttps://hdl.handle.net/20.500.12415/7987
dc.identifier.volume32en_US
dc.identifier.wosWOS:000439421100034en_US
dc.identifier.wosqualityQ2en_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.snmzKY01030
dc.subjectSequencesen_US
dc.subjectseriesen_US
dc.subjectsummabilityen_US
dc.subjectcontinuityen_US
dc.titleBeyond Cauchy and Quasi-Cauchy Sequencesen_US
dc.typeArticle
dspace.entity.typePublication

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