Lacunary ward continuity in 2-normed spaces

Huseyin Cakalli, Sibel Ersan

In this paper, we introduce lacunary statistical ward continuity in a 2-normed space. A function $f$ defined on a subset $E$ of a 2-normed space $X$ is lacunary statistically ward continuous if it preserves lacunary statistically quasi-Cauchy sequences of points in $E$ where a sequence ($x_k$) of points in $X$ is lacunary statistically quasi-Cauchy if \[ im_{roıfty}\frac1{h_r}|\{kı I_r:\|x_{k+1}-x_k,z\|\geqǎrepsilon\}|=0 \] for every positive real number $\varepsilon$ and $z\in X$, and $(k_r)$ is an increasing sequence of positive integers such that $k_0=0$ and $h_r=k_r-k_{r-1}\to\infty$ as $r\to\infty$, $I_r=(k_{r-1},k_r]$. We investigate not only lacunary statistical ward continuity, but also some other kinds of continuities in 2-normed spaces.