Quasi Cauchy double sequences

R. F. Patterson and H. Cakalli

A double sequence {xk,l} is quasi-Cauchy if given an ε > 0 there exists an N ϵ N such that
maxr,s=1and/or 0{ |xk,l - xk+r,l+s| } < ε.
We study continuity type properties of factorable double functions defined on a double subset A×A of R2 into 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×A of R2 into R.

Tbilisi Mathematical Journal, Vol. 8(2) (2015), pp. 211-219