Consistent classes of double summability methods (Q979150)

The four dimensional matrix \(A\) is said to be RH-regular if it maps every bounded P-convergent sequence into a P-convergent sequence with the same P-limit. The first author [\textit{R F. Patterson}, Int. J. Math. Math. Sci. 23, No.~1, 1--9 (2000; Zbl 0954.40005)] proved that if a bounded double sequence is divergent then there are RH-regular matrix methods that sum it to various values. The authors then ask the following question in this paper: Is there a collection \(\gamma\) of RH-regular matrix methods which are consistent and such that every bounded double sequence is summable by at least one method in the collection? They mention how difficult it is to find all such collections. However, they have extended this class to a countable collection of RH-regular matrix methods with bounded norm.