标题：On the consistency of limitation methods for <mml:math alttext="$(N, p_n)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math> summable sequences
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1981
卷号：4
DOI：10.1155/S0161171281000112
出版社：Hindawi Publishing Corporation
摘要：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.
