N-theta-Ward Continuity
| dc.authorid | 0000-0001-7344-5826 | en_US |
| dc.contributor.author | Cakalli, Huseyin | |
| dc.date.accessioned | 2024-07-12T21:44:11Z | |
| dc.date.available | 2024-07-12T21:44:11Z | |
| dc.date.issued | 2012 | en_US |
| dc.department | Maltepe Üniversitesi | en_US |
| dc.description.abstract | A function f is continuous if and only if f preserves convergent sequences; that is, (f(alpha(n))) is a convergent sequence whenever (alpha(n)) is convergent. The concept of N-theta-ward continuity is defined in the sense that a function f is N-theta-ward continuous if it preserves N-theta-quasi-Cauchy sequences; that is, (f(alpha(n))) is an N-theta-quasi-Cauchy sequence whenever (alpha(n)) is N-theta-quasi-Cauchy. A sequence (alpha(k)) of points in R, the set of real numbers, is N-theta-quasi-Cauchy if lim(r ->infinity) (1/h(r)) Sigma(k is an element of Ir) vertical bar Delta alpha(k)vertical bar = 0, where Delta alpha(k) = alpha(k+1) - alpha(k), 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) = 0 and h(r) : k(r) - k(r-1) -> infinity. A new type compactness, namely, N-theta-ward compactness, is also, defined and some new results related to this kind of compactness are obtained. | en_US |
| dc.identifier.doi | 10.1155/2012/680456 | |
| dc.identifier.issn | 1085-3375 | |
| dc.identifier.issn | 1687-0409 | |
| dc.identifier.scopus | 2-s2.0-84863653282 | en_US |
| dc.identifier.scopusquality | Q4 | en_US |
| dc.identifier.uri | https://dx.doi.org/10.1155/2012/680456 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12415/7691 | |
| dc.identifier.wos | WOS:000305612400001 | 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 | HINDAWI LTD | en_US |
| dc.relation.ispartof | ABSTRACT AND APPLIED ANALYSIS | 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 | KY00016 | |
| dc.title | N-theta-Ward Continuity | en_US |
| dc.type | Article | |
| dspace.entity.type | Publication |
