On sequences in 2-normed spaces

Abstract

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 $li{m}_{n\to \infty }||\Delta x_n,z||=0$ 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.

15 pages