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On summability factors for \(|\overline N, p_n|_k\). (English) Zbl 1120.40002

The authors generalize the result of N. Singh and N. Sharma [Proc. Indian Acad. Sci., Math. Sci. 110, 61-68 (2000; Zbl 0946.40002)]. They prove necessary and sufficient conditions for \(\sum a_{n}\lambda _{n}\) to be \( \left| N,q\right| _{k}\) summable with \(k>1,\) whenever \(\sum a_{n}\) is \(\left| N,p,q\right| _{k}\)summable. There are no definitions of \(\left| N,q\right| _{k}\) and \(\left| N,p,q\right| _{k}\) methods.

MSC:

40D15 Convergence factors and summability factors
40D25 Inclusion and equivalence theorems in summability theory
40F05 Absolute and strong summability

Citations:

Zbl 0946.40002
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