## 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

### Keywords:

weighted means; non-Archimedean fields; summability methods

Zbl 0128.28004
Full Text:

### References:

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