Weighted means in non-Archimedean fields (Q1898753)

\textit{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 \(p\).