Ward Continuity in 2-Normed Spaces

Sibel Ersan, Hüseyin Čakalli

In this paper, we introduce and investigate the concept of 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 $\lim_{n\to\infty}\|\Delta x_n,z\|=0$ for every $z\in X$. Some other kinds of continuities are also introduced, and interesting theorems are proved in 2-normed spaces.