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arXiv · 2211.16026

A variation of continuity in $n$-normed spaces

Sibel Ersan
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Abstract

The s-th forward difference sequence that tends to zero, inspired by the consecutive terms of a sequence approaching zero, is examined in this study. Functions that take sequences satisfying this condition to sequences satisfying the same condition are called s-ward continuous. Inclusion theorems that are related to this kind of uniform continuity and continuity are also considered. Additionally, the concept of $s$-ward compactness of a subset of $X$ via $s$-quasi-Cauchy sequences are investigated. One finds out that the uniform limit of any sequence of $s$-ward continuous function is $s$-ward continuous and the set of $s$-ward continuous functions is a closed subset of the set of continuous functions.

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Sibel Ersan. 2022-11-29. A variation of continuity in $n$-normed spaces. https://arxiv.org/abs/2211.16026

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