Ward continuity in 2-normed spaces

A function $f$ defined on a $2$-normed space $ (X,||.,.||)$  is ward continuous if it preserves quasi-Cauchy sequences where a sequence $(x_n)$  of points in $X$ is called quasi-Cauchy if  $lim_{n\rightarrow\infty}||\Delta x_{n},z||=0$ for every $z\in X$. Some other kinds of continuties are also introduced via quasi-Cauchy sequences in $2$-normed spaces. It turns out that uniform limit of ward continuous functions is again ward continuous.