Variations on strong lacunary quasi-Cauchy sequences

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dc.authorid0000-0001-7344-5826en_US
dc.contributor.authorKaplan, Huseyin
dc.contributor.authorCakalli, Huseyin
dc.date.accessioned2024-07-12T21:51:07Z
dc.date.available2024-07-12T21:51:07Z
dc.date.issued2016en_US
dc.departmentMaltepe Üniversitesien_US
dc.description.abstractWe introduce a new function space, namely the space of N-theta(alpha)(p)-ward continuous functions, which turns out to be a closed subspace of the space of continuous functions. A real valued function f defined on a subset A of R, the set of real numbers, is N-theta(alpha)(p)-ward continuous if it preserves N-theta(alpha)(p)-quasi-Cauchy sequences, that is, (f(x(n))) is an N-theta(alpha)(p)-quasi-Cauchy sequence whenever (x(n)) is N-theta(alpha)(p)-quasi-Cauchy sequence of points in A, where a sequence (x(k)) of points in R is called N-theta(alpha)(p)-quasi-Cauchy if lim(r ->infinity) 1/h(r)(alpha) Sigma(k is an element of lr) vertical bar Delta x(k)vertical bar(p) = 0, where Delta x(k) = x(k+1) - x(k) for each positive integer k, p is a constant positive integer, alpha is a constant in ]0,1], I-r = (k(r-1), k(r)] and theta = (k(r)) is a lacunary sequence, that is, an increasing sequence of positive integers such that k(0) not equal 0, and h(r) : k(r) - k(r-1) -> infinity. Some other function spaces are also investigated. (C) 2016 All rights reserved.en_US
dc.identifier.endpage4380en_US
dc.identifier.issn2008-1898
dc.identifier.issn2008-1901
dc.identifier.issue6en_US
dc.identifier.scopus2-s2.0-84990030917en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.startpage4371en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12415/8242
dc.identifier.volume9en_US
dc.identifier.wosWOS:000386871300077en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherINT SCIENTIFIC RESEARCH PUBLICATIONSen_US
dc.relation.ispartofJOURNAL OF NONLINEAR SCIENCES AND APPLICATIONSen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmzKY01994
dc.subjectSummabilityen_US
dc.subjectstrongly lacunary convergenceen_US
dc.subjectquasi-Cauchy sequencesen_US
dc.subjectboundednessen_US
dc.subjectuniform continuityen_US
dc.titleVariations on strong lacunary quasi-Cauchy sequencesen_US
dc.typeArticle
dspace.entity.typePublication

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