On the consistency of limitation methods for(N,pn)summable sequences
1981 ◽
Vol 4
(1)
◽
pp. 155-164
Keyword(s):
Two limitation methods,AandB, are said to be consistent for a classbof sequences, iff, every sequence belonging tobis limitable both byAandBand that theA-limit equals theB-limit. Any two regular limitation methods are consistent for the class-cof convergent sequences. However, this is not true in general and in fact, corresponding to every bounded non-convergent sequence it is possible to determine twoT-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.
2013 ◽
Vol 88
(2)
◽
pp. 232-242
◽
1972 ◽
Vol 13
(1)
◽
pp. 82-90
◽
2020 ◽
Vol 13
(5)
◽
pp. 1088-1096
2000 ◽
Vol 24
(8)
◽
pp. 533-538
1996 ◽
Vol 54
(2)
◽
pp. 197-202
◽
1986 ◽
Vol 23
(04)
◽
pp. 851-858
◽
1991 ◽
Vol 11
(1)
◽
pp. 65-71
◽