Necessary and sufficient conditions for inclusion relations for absolute summability

Details Necessary and sufficient conditions for inclusion relations for absolute summability Necessary and sufficient conditions for inclusion relations for absolute summability

2003-09-25

arxiv.org/abs/math/0309419v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 3, August 2003, pp. 243-250

Mathematics

Classical Analysis and ODEs

8 pages, no figures

Scientific paper

We obtain a set of necessary and sufficient conditions for $| \bar{N}, p_{n}
|_{k} $ to imply $|\bar{N}, q_{n} |_{s}$ for $1 < k \leq s < \infty$. Using
this result we establish several inclusion theorems as well as conditions for
the equivalence of $| \bar {N}, p_{n} |_{k}$ and $|\bar{N},q_{n} |_{s}$.

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