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Weighted means in non-Archimedean fields. (English) Zbl 0836.40003

V. K. Srinivasan [Nederl. Akad. Wet., Proc., Ser. A 68, 319-325 (1965; Zbl 0128.28004)] defined the analogue of the classical weighted means \((\overline {N}, p_n)\) in non-Archimedean fields under the assumption on the sequence \(\{p_n\}\) of weights that \(|p_0 |< |p_1|< \dots< |p_n |< \dots\) and \(\lim|p_n |= \infty\). In the present paper the author proves five theorems establishing regularity and limitation theorems, inclusion theorems of \((\overline {N}, p_n)\), and he also establishes the comparison with a regular matrix and regular triangular matrix. Further the author obtains a strictly increasing scale of regular summability methods in \(\mathbb{Q}_p\), the \(p\)-adic field for a prime \(p\).
Reviewer: I.L.Sukla (Orissa)

MSC:

40G99 Special methods of summability

Citations:

Zbl 0128.28004
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References:

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[6] V.K. Srinivasan , On certain summation processes in the p-adic field , Indag. Math. 27 ( 1965 ) , 368 - 374 . MR 196334 | Zbl 0128.28004 · Zbl 0128.28004
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