Cakalli, Huseyin2024-07-122024-07-1220150354-518010.2298/FIL1501013C2-s2.0-84928963873https://dx.doi.org/10.2298/FIL1501013Chttps://hdl.handle.net/20.500.12415/7992In this paper, we introduce and study new kinds of continuities. It turns out that a function f defined on an interval is uniformly continuous if and only if there exists a positive integer p such that f preserves p-quasi-Cauchy sequences where a sequence (x(n)) is called p-quasi-Cauchy if the sequence of differences between p-successive terms tends to 0.eninfo:eu-repo/semantics/closedAccesssequencesseriessummabilityreal functionscontinuitycompactnessArticle191Q31329WOS:000355844100004Q3