Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-20T01:24:51.319Z Has data issue: false hasContentIssue false
  • English
  • Français

On generalized Nörlund methods of summability

Published online by Cambridge University Press:  17 April 2009

Minoru Tanaka
Minoru Tanaka
Affiliation:
Department of Mathematics, Faculty of Science, Chiba University, Chiba, Japan.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The object of this paper is to establish some relations between two generalized Nörlund methods and also between two absolute generalized Nörlund methods. Our theorems obtained here generalize many known results, including McFadden's Theorems which state the inclusion relations between two absolute Nörlund methods, and results of Ikuko Kayashima.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 3 , December 1978 , pp. 381 - 402
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Borwein, D., “On products of sequences”, J. London Math. Soc. 33 (1958), 352–357.CrossRefGoogle Scholar
[2]Borwein, D. and Cass, F.P., “Strong Nörlund summability”, Math. Z. 103 (1968), 94–111.CrossRefGoogle Scholar
[3]Das, G., “On some methods of summability”, Quart. J. Math. Oxford Ser. 17 (1966), 244–256.CrossRefGoogle Scholar
[4]Das, G.. “On some methods of summability (II)”, Quart. J. Math. Oxford Ser. 19 (1968), 417–431.Google Scholar
[5]Dikshit, G.D., “On inclusion relation between Riesz and Nörlund means”, Indian J. Math. 7(1965), 73–81.Google Scholar
[6]Hardy, G.H., Divergent series (Clarendon Press, Oxford, 1949).Google Scholar
[7]Kayashima, Ikuko, “On relations between Nörlund and Riesz means”, Pacific J. Math. 49 (1973), 391–396.CrossRefGoogle Scholar
[8]Kayashima, Ikuko, “Inclusion theorems for absolute Nörlund summability”, submitted.Google Scholar
[9]Kuttner, Brian and Rhoades, B.E., “Relations between (N, Pn) and (Ñ, Pn) summability” Proc. Edinburgh Math. Soc. (2) 16 (1968), 109–116.CrossRefGoogle Scholar
[10]Lorch, Lee, “Supplement to a theorem of Cesàro”, Scripta Math. 23 (1957), 163–165.Google Scholar
[11]McFadden, Leonard, “Absolute Nörlund summability”, Duke Math. J. 9 (1942), 168–207.Google Scholar
[12]Mears, Florence M., “Absolute regularity and Nörlund mean”, Ann. of Math. (2) 38 (1937), 594–601.Google Scholar
[13]Rhoades, B.E., “On the total inclusion for Nörlund methods of summability”, Math. Z. 96 (1967), 183–188.Google Scholar
[14]Rhoades, Billy E., “On the total inclusion for Nörlund methods of summability. II”, Math. Z. 113 (1970), 171–172.CrossRefGoogle Scholar
[15]Sunouchi, Gen-ichirô, “Notes on Fourier analysis (XVIII): absolute summability of series with constant terms”, Tôhoku Math. J. (2) 1 (1949), 57–65.CrossRefGoogle Scholar