No CrossRef data available.
A note on the strong regularity of Nrlund means
Published online by Cambridge University Press: 24 October 2008
Extract
Let (pn), (qn) and (un) be sequences of real or complex numbers with
The sequence (sn) is strongly generalized Nrlund summable with index 0, to s, or s or snsN, p, Q if
and pnv=pnvpnv1, with p10. Strong Nrlund summability N, p was first studied by Borweing and Cass (1), and its generalization N, p, Q by Thorp (6). We shall say that (sn) is strongly generalized convergent of index 0, to s, and write snsC, 0, Q if sns and 
where sn=a0+a1++an. When qn all n, this definition reduces to strong convergence of index , introduced by Hyslop (4). If 
as n, the sequence (sn) is summable (
, q) to s sns(, q).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 2 , September 1983 , pp. 261 - 263
- Copyright
- Copyright © Cambridge Philosophical Society 1983
References
REFERENCES
(1)Borwein, D. and Cass, F. P.Strong Nrlund summability. Math. Z. 103 (1968), 94111.CrossRefGoogle Scholar
(2)Das, G. On some methods of summability (II). Quart. J. Math. Oxford Ser 19 (1968), 417431.CrossRefGoogle Scholar
(4)Hyslop, J. M.Note on the strong summability of series. Proc. Glasgow Math. Assoc. 1 (1952), 1620.CrossRefGoogle Scholar
(5)Kuttner, B.Some theorems on the strong regularity of Nrlund methods. Proc. Cambridge Philos. Soc. 76 (1974), 195209.CrossRefGoogle Scholar