论文标题
$ n $ normed空间中的连续性变化
A variation of continuity in $n$-normed spaces
论文作者
论文摘要
在本研究中检查了趋于零的第二个向前差序列，灵感来自接近零的序列的连续项。采用满足此条件以满足相同条件的序列的序列的函数称为s-ward连续。还考虑了与这种统一的连续性和连续性相关的包含定理。此外，研究了$ s $ ward的概念通过$ s $ quasi-cauchy序列的$ x $的$ x $。人们发现，$ s $ - 沃德连续功能的任何序列的均匀限制是$ s $ - 沃德连续的，$ s $ - 沃德连续函数的集合是连续函数集的封闭子集。
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.
