Variations on strong lacunary quasi-Cauchy sequences
| dc.authorid | 0000-0001-7344-5826 | |
| dc.contributor.author | Kaplan, Huseyin | |
| dc.contributor.author | Cakalli, Huseyin | |
| dc.date.accessioned | 2019-08-01T13:38:39Z | |
| dc.date.available | 2019-08-01T13:38:39Z | |
| dc.date.issued | 2016 | |
| dc.department | Niğde ÖHÜ | |
| dc.description.abstract | We 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. | |
| dc.identifier.endpage | 4380 | |
| dc.identifier.issn | 2008-1898 | |
| dc.identifier.issn | 2008-1901 | |
| dc.identifier.issue | 6 | |
| dc.identifier.scopus | 2-s2.0-84990030917 | |
| dc.identifier.scopusquality | N/A | |
| dc.identifier.startpage | 4371 | |
| dc.identifier.uri | https://hdl.handle.net/11480/3771 | |
| dc.identifier.volume | 9 | |
| dc.identifier.wos | WOS:000386871300077 | |
| dc.identifier.wosquality | Q1 | |
| dc.indekslendigikaynak | Web of Science | |
| dc.indekslendigikaynak | Scopus | |
| dc.institutionauthor | [0-Belirlenecek] | |
| dc.language.iso | en | |
| dc.publisher | INT SCIENTIFIC RESEARCH PUBLICATIONS | |
| dc.relation.ispartof | JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/closedAccess | |
| dc.subject | Summability | |
| dc.subject | strongly lacunary convergence | |
| dc.subject | quasi-Cauchy sequences | |
| dc.subject | boundedness | |
| dc.subject | uniform continuity | |
| dc.title | Variations on strong lacunary quasi-Cauchy sequences | |
| dc.type | Article |
