On the consistency of limitation methods for ( N, p n ) summable sequences

Nand Kishore and U. K. Misra

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-10

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 , p n ) summable sequences.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:357817

DOI: 10.1155/S0161171281000112

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