A Study on Strongly Lacunary Ward Continuity in 2-Normed Spaces

In this paper, we study the ideal strong lacunary ward compactness of a subset of a 2-normed space $X$ and the ideal strongly lacunary ward continuity of a function $f$ on $X$. Here a subset $E$ of $X$ is said to be ideal strong lacunary ward compact if any sequence in $E$ has an ideal strong lacunary quasi-Cauchy subsequence. Additionally, a function on $X$ is said to be ideal strong lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences; an ideal is defined to be a hereditary and additive family of subsets of $\mathbb{N}$. We find that a subset $E$ of $X$ with a countable Hamel basis is totally bounded if and only if it is ideal strong lacunary ward compact.