On quasi Cauchy double sequences in metric spaces

A double sequence x={xk,l} in a metric space X is quasi-Cauchy if given an ε>0 there exists an N∈N such that d(xk,l,xk+1,l+1),d(xk,l,xk+1,l),d(xk,l,xk,l+1)<ε for k,l>N. We study continuity type properties of factorable double functions defined on a double subset E×E of X2 into X, and obtain interesting results related to compactness, uniform continuity, sequential continuity, continuity, and a newly introduced type of continuity of factorable double functions defined on a double subset E×E of X2 into X.