Statistical quasi-Cauchy sequences
| dc.authorid | 0000-0001-7344-5826 | en_US |
| dc.contributor.author | Cakalli, Huseyin | |
| dc.date.accessioned | 2024-07-12T21:51:52Z | |
| dc.date.available | 2024-07-12T21:51:52Z | |
| dc.date.issued | 2011 | en_US |
| dc.department | Maltepe Üniversitesi | en_US |
| dc.description.abstract | A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (x(n)) statistically quasi-Cauchy if st - lim(n ->infinity) d(x(n+1), x(n)) = 0, and lacunary statistically quasi-Cauchy if S-theta - lim(n ->infinity) d(x(n+1), x(n)) = 0. We prove that a subset E of a metric space is totally bounded if and only if any sequence of points in E has a subsequence which is any type of the following: statistically quasi-Cauchy, lacunary statistically quasi-Cauchy, quasi-Cauchy, and slowly oscillating. It turns out that a function defined on a connected subset E of a metric space is uniformly continuous if and only if it preserves either quasi-Cauchy sequences or slowly oscillating sequences of points in E. (C) 2011 Elsevier Ltd. All rights reserved. | en_US |
| dc.identifier.doi | 10.1016/j.mcm.2011.04.037 | |
| dc.identifier.endpage | 1624 | en_US |
| dc.identifier.issn | 0895-7177 | |
| dc.identifier.issn | 1872-9479 | |
| dc.identifier.issue | 05.Jun | en_US |
| dc.identifier.scopus | 2-s2.0-79957867673 | en_US |
| dc.identifier.scopusquality | N/A | en_US |
| dc.identifier.startpage | 1620 | en_US |
| dc.identifier.uri | https://dx.doi.org/10.1016/j.mcm.2011.04.037 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12415/8326 | |
| dc.identifier.volume | 54 | en_US |
| dc.identifier.wos | WOS:000291243300037 | en_US |
| dc.identifier.wosquality | Q1 | en_US |
| dc.indekslendigikaynak | Web of Science | |
| dc.indekslendigikaynak | Scopus | |
| dc.institutionauthor | Cakalli, Huseyin | |
| dc.language.iso | en | en_US |
| dc.publisher | PERGAMON-ELSEVIER SCIENCE LTD | en_US |
| dc.relation.ispartof | MATHEMATICAL AND COMPUTER MODELLING | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.snmz | KY02869 | |
| dc.subject | Quasi-Cauchy sequences | en_US |
| dc.subject | Slowly oscillating sequences | en_US |
| dc.subject | Summability | en_US |
| dc.subject | Total boundedness | en_US |
| dc.subject | Uniform continuity | en_US |
| dc.title | Statistical quasi-Cauchy sequences | en_US |
| dc.type | Article | |
| dspace.entity.type | Publication |
