A Variation on Statistical Ward Continuity

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dc.authorid0000-0001-7344-5826en_US
dc.contributor.authorCakalli, Huseyin
dc.date.accessioned2024-07-12T21:45:21Z
dc.date.available2024-07-12T21:45:21Z
dc.date.issued2017en_US
dc.departmentMaltepe Üniversitesien_US
dc.description.abstractA sequence (alpha(k)) of points in R, the set of real numbers, is called rho-statistically convergent to an element l of R if lim (n ->infinity) 1/rho n |{k <= n : |alpha(k)-l| >= epsilon}| = 0 for each epsilon > 0, where rho = (rho n) is a non-decreasing sequence of positive real numbers tending to 8 such that lim sup(n) rho n/n < infinity, Delta rho n = O(1), and Delta alpha(n) = alpha(n+ 1) - alpha(n) for each positive integer n. A real-valued function defined on a subset of R is called rho-statistically ward continuous if it preserves rho-statistical quasi-Cauchy sequences where a sequence (alpha(k)) is defined to be rho-statistically quasi-Cauchy if the sequence (Delta alpha(k)) is rho-statistically convergent to 0. We obtain results related to rho-statistical ward continuity, rho-statistical ward compactness, ward continuity, continuity, and uniform continuity. It turns out that the set of uniformly continuous functions coincides with the set of rho-statistically ward continuous functions not only on a bounded subset of R, but also on an interval.en_US
dc.identifier.doi10.1007/s40840-015-0195-0
dc.identifier.endpage1710en_US
dc.identifier.issn0126-6705
dc.identifier.issn2180-4206
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85031773200en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage1701en_US
dc.identifier.urihttps://dx.doi.org/10.1007/s40840-015-0195-0
dc.identifier.urihttps://hdl.handle.net/20.500.12415/7826
dc.identifier.volume40en_US
dc.identifier.wosWOS:000412926000019en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorCakalli, Huseyin
dc.language.isoenen_US
dc.publisherMALAYSIAN MATHEMATICAL SCIENCES SOCen_US
dc.relation.ispartofBULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETYen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmzKY00457
dc.subjectSummabilityen_US
dc.subjectStatistical convergent sequencesen_US
dc.subjectQuasi-Cauchy sequencesen_US
dc.subjectBoundednessen_US
dc.subjectUniform continuityen_US
dc.titleA Variation on Statistical Ward Continuityen_US
dc.typeArticle
dspace.entity.typePublication

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