Two valued measure and summability of double sequences in asymmetric context (Q626062)

The distance function \(d\) in an asymmetric metric space \((X,d)\) satisfies \(d(x,y)\geq0\), \(d(x,y)=0\) iff \(x=y\), \(d(x,z)\leq d(x,y)+d(y,z)\), but \(d(x,y)\) need not be equal to \(d(y,x)\). Various kinds of convergence or divergence of double sequences are examined in asymmetric metric spaces satisfying a special ``approximate metric axiom'' (AMA) involving a function \(c(x,y)\) such that \(d(x,y)\leq c(x,y)d(y,x)\) for all \(x,y\) in \(X\) and some further boundedness restrictions. The ideas of the authors' earlier paper [Czech. Math. J. 59, 1141--1155 (2009; Zbl 1224.40009)] are extended to double sequences in AMA asymmetric metric spaces.