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A note on the strong regularity of Nrlund means

Published online by Cambridge University Press:  24 October 2008

J. R. Nurcombe
Affiliation:
Hall Green Technical College, Colebank Road, Birmingham 28

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
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

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