  The main object of this paper is to investigate $\lambda$-statistically
quasi-Cauchy sequences. A real valued function $f$ defined on a subset $E$ of
$\textbf{R}$, the set of real numbers, is called $\lambda$-statistically ward
continuous on $E$ if it preserves $\lambda$-statistically quasi-Cauchy
sequences of points in $E$. It turns out that uniform continuity coincides with
$\lambda$-statistically ward continuity on $\lambda$-statistically ward compact
subsets.
