Variations on Quasi-Cauchy Sequences

Hüseyin Çakallı

In 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.