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

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  • Nand Kishore
  • U. K. Misra

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.

Suggested Citation

  • Nand Kishore & U. K. Misra, 1981. "On the consistency of limitation methods for ( N , p n ) summable sequences," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 4, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:357817
    DOI: 10.1155/S0161171281000112
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