Natarajan, P. N. On Nörlund method of summability in non-Archimedean fields. (English) Zbl 0807.40005 J. Anal. 2, 97-102 (1994). V. K. Srinivasan [Nederl. Akad. Wet., Proc., Ser. A 68, 319-325 (1965; Zbl 0128.280)] introduced summation methods in a complete nontrivial valued, non-Archimedean field where he has proved that \(p_ n \to 0\) as \(n \to \infty\) is a sufficient condition for \((N, p_ n)\) to be regular. In this paper the author establishes that the condition is also necessary for regularity. Further he establishes the consistency and equivalence of two Nörlund methods. Reviewer: I.L.Sukla (Orissa) Cited in 3 Documents MSC: 40J05 Summability in abstract structures 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis 40G05 Cesàro, Euler, Nörlund and Hausdorff methods 12J25 Non-Archimedean valued fields Keywords:summability method; Nörlund summability; non-Archimedean functional analysis; non-Archimedean field Citations:Zbl 0128.280 PDFBibTeX XMLCite \textit{P. N. Natarajan}, J. Anal. 2, 97--102 (1994; Zbl 0807.40005)