Functions preserving slowly oscillating double sequences

Abstract

A double sequence $\text{x}=\{x_{k,l}\}$ of points in $\text{R}$ is slowly oscillating if for any given $\epsilon >0$, there exist $\alpha =\alpha (\epsilon )>0$, $\delta =\delta (\epsilon )>0$, and $N=N(\epsilon )$ such that $|x_{k,l}-x_{s,t}|<\epsilon$ whenever $k,l\ge N(\epsilon )$ and $k\le s\le (1+\alpha )k$, $l\le t\le (1+\delta )l$. We study continuity type properties of factorable double functions defined on a double subset $A\times A$ of ${\text{R}}^2$ into $\text{R}$, and obtain interesting results related to uniform continuity, sequential continuity, and a newly introduced type of continuity of factorable double functions defined on a double subset $A\times A$ of ${\text{R}}^2$ into $\text{R}$.

11 pages. arXiv admin note: substantial text overlap with arXiv:1312.6602

Cited by in corpus (3)

• A study on downward half Cauchy sequences
• On Abel statistical convergence
• On Variations of statistical ward continuity