International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 1, Pages 155-164
doi:10.1155/S0161171281000112
Abstract
Two limitation methods, A and B, are said to be consistent for a class b of sequences, iff, every sequence belonging to b is limitable both by A and B and that the A-limit equals the B-limit. Any two regular limitation methods are consistent for the class-c of convergent sequences. However, this is not true in general and in fact, corresponding to every bounded non-convergent sequence it is possible to determine two T-matrices such that they limit the sequence to two different values. In this paper, we establish the necessary and sufficient conditions for the consistency of two limitation methods, for (N,pn) summable sequences.