Ideal quasi-Cauchy sequences
| dc.authorid | 0000-0001-7344-5826 | en_US |
| dc.authorid | 0000-0002-0644-0600 | en_US |
| dc.contributor.author | Cakalli, Huseyin | |
| dc.contributor.author | Hazarika, Bipan | |
| dc.date.accessioned | 2024-07-12T21:50:45Z | |
| dc.date.available | 2024-07-12T21:50:45Z | |
| dc.date.issued | 2012 | en_US |
| dc.department | Maltepe Üniversitesi | en_US |
| dc.description.abstract | An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. A sequence (x(n)) of real numbers is said to be I-convergent to a real number L if for each epsilon > 0, the set {n : vertical bar x(n) - L vertical bar >= epsilon} belongs to I. We introduce I-ward compactness of a subset of R, the set of real numbers, and I-ward continuity of a real function in the senses that a subset E of R is I-ward compact if any sequence (x(n)) of points in E has an I-quasi-Cauchy subsequence, and a real function is I-ward continuous if it preserves I-quasi-Cauchy sequences where a sequence (x(n)) is called to be I-quasi-Cauchy when (Delta x(n)) is I-convergent to 0. We obtain results related to I-ward continuity, I-ward compactness, ward continuity, ward compactness, ordinary compactness, ordinary continuity, delta-ward continuity, and slowly oscillating continuity. | en_US |
| dc.identifier.doi | 10.1186/1029-242X-2012-234 | |
| dc.identifier.issn | 1029-242X | |
| dc.identifier.scopus | 2-s2.0-84873393080 | en_US |
| dc.identifier.scopusquality | Q2 | en_US |
| dc.identifier.uri | https://dx.doi.org/10.1186/1029-242X-2012-234 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12415/8200 | |
| dc.identifier.wos | WOS:000317842500001 | en_US |
| dc.identifier.wosquality | Q1 | en_US |
| dc.indekslendigikaynak | Web of Science | |
| dc.indekslendigikaynak | Scopus | |
| dc.language.iso | en | en_US |
| dc.publisher | SPRINGER INTERNATIONAL PUBLISHING AG | en_US |
| dc.relation.ispartof | JOURNAL OF INEQUALITIES AND APPLICATIONS | 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 | KY01920 | |
| dc.subject | ideal | en_US |
| dc.subject | continuity | en_US |
| dc.subject | summability | en_US |
| dc.subject | compactness | en_US |
| dc.title | Ideal quasi-Cauchy sequences | en_US |
| dc.type | Article | |
| dspace.entity.type | Publication |
