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.

Comment: 11 pages. arXiv admin note: substantial text overlap with arXiv:1205.3674, arXiv:1102.1531