Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-27T09:56:44.883Z Has data issue: false hasContentIssue false
  • English
  • Français

Limitation theorems for some 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 280, 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 limitation theorems for the ordinary and also absolute generalized Nörlund methods which include some known results as special cases. We shall give a different proof of the recent result of S. Narang (Proc. Indian Acad. Sci. Sect. A 88 (1979), 115–123), and we get a generalization of the result of G. Das (J. London Math. Soc. 41 (1966), 685–692) which states the summability factors of the absolute Nörlund methods.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 3 , December 1980 , pp. 373 - 384
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Das, G., “On the absolute Nörlund summability factors of infinite series”, J. London Math. Soc. 41 (1966), 685–692.CrossRefGoogle Scholar
[2]Das, G., “On some methods of summability”, Quart. J. Math. Oxford Ser. 17 (1966), 244–256.CrossRefGoogle Scholar
[3]Hardy, G.H., Divergent series (Clarendon Press, Oxford, 1949).Google Scholar
[4]Kishore, Nand, “A limitation theorem for absolute Nörlund summability”, J. London Math. Soc. (2) 4 (1971/1972), 240–244.CrossRefGoogle Scholar
[5]Mohanty, R., “On the absolute Riesz summability of Fourier series and allied series”, Proc. London Math. Soc. (2) 52 (1951), 295–320.Google Scholar
[6]Narang, S., “Limitation theorems for absolute Nörlund summability”, Proc. Indian Acad. Sci. Sect. A 88 (1979), 115–123.CrossRefGoogle Scholar
[7]Peyerimhoff, A., Lectures on summability (Lecture Notes in Mathematics, 107. Springer-Verlag, Berlin, Heidelberg, New York, 1969).CrossRefGoogle Scholar