Çakallı, Hüseyin2024-07-122024-07-122011Çakallı, H. (2011). ?-quasi-Cauchy sequences. Mathematical and Computer Modelling. 53(1-2), 397-401.10.1016/j.mcm.2010.09.0102-s2.0-77958511660https://www.sciencedirect.com/science/article/pii/S0895717710004413?via%3Dihubhttps://doi.prg/10.1016/j.mcm.2010.09.010https://hdl.handle.net/20.500.12415/2960Recently, it has been proved that a real-valued function defined on a subset E of R, the set of real numbers, is uniformly continuous on E if and only if it is defined on E and preserves quasi-Cauchy sequences of points in E where a sequence is called quasi-Cauchy if (?xn) is a null sequence. In this paper we call a real-valued function defined on a subset E of R?-ward continuous if it preserves ?-quasi-Cauchy sequences where a sequence x=(xn) is defined to be ?-quasi-Cauchy if the sequence (?xn) is quasi-Cauchy. It turns out that ?-ward continuity implies uniform continuity, but there are uniformly continuous functions which are not ?-ward continuous. A new type of compactness in terms of ?-quasi-Cauchy sequences, namely ?-ward compactness is also introduced, and some theorems related to ?-ward continuity and ?-ward compactness are obtained.eninfo:eu-repo/semantics/openAccessReal functionsContinuitySequencesLetter4011.Şub39753WOS:000284659800035Q1