On sequences in 2-normed spaces

Sibel Ersan; Huseyin Cakalli

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arXiv · 1306.2469

On sequences in 2-normed spaces

Sibel Ersan·Huseyin Cakalli

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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 $lim_{n\rightarrow\infty}||Δx_{n},z||=0$ 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.

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BibTeX RIS

Sibel Ersan, Huseyin Cakalli. 2013-07-19. On sequences in 2-normed spaces. https://arxiv.org/abs/1306.2469

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