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International Journal of Mathematics and Mathematical Sciences
Volume 4, Issue 1, Pages 155-164
http://dx.doi.org/10.1155/S0161171281000112

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

Department of Mathematics, Berhampur University, Berhampur 760007, Orissa, India

Received 8 November 1978; Revised 12 March 1979

Copyright © 1981 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.