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December 2015 Quasi Cauchy double sequences
Richard F. Patterson, Huseyin Cakalli
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Tbilisi Math. J. 8(2): 211-219 (December 2015). DOI: 10.1515/tmj-2015-0023

Abstract

A double sequence $\{x_{k,l}\}$ is quasi-Cauchy if given an $\epsilon \gt 0$ there exists an $N \in {\bf N}$ such that $$\max_{r,s= 1\mbox{ and/or } 0} \left \{|x_{k,l} - x_{k+r,l+s}|\right \} \lt \epsilon .$$ We study continuity type properties of factorable double functions defined on a double subset $A\times A$ of ${\bf R}^{2}$ into $\textbf{R}$, and obtain interesting results related to uniform continuity, sequential continuity, continuity, and a newly introduced type of continuity of factorable double functions defined on a double subset $A\times A$ of ${\bf R}^{2}$ into $\textbf{R}$.

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Richard F. Patterson. Huseyin Cakalli. "Quasi Cauchy double sequences." Tbilisi Math. J. 8 (2) 211 - 219, December 2015. https://doi.org/10.1515/tmj-2015-0023

Information

Received: 5 August 2015; Accepted: 30 August 2015; Published: December 2015
First available in Project Euclid: 12 June 2018

zbMATH: 1343.40006
MathSciNet: MR3420405
Digital Object Identifier: 10.1515/tmj-2015-0023

Subjects:
Primary: 40B05
Secondary: 40C05

Rights: Copyright © 2015 Tbilisi Centre for Mathematical Sciences

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Vol.8 • No. 2 • December 2015
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