Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-25T06:10:00.436Z Has data issue: false hasContentIssue false

Strong and absolute summabilities of functions based on (D, α) summability methods

Published online by Cambridge University Press:  24 October 2008

Babban Prasad Mishra
Affiliation:
The University, Gorakhpur, India
Anand Prakash Srivastava
Affiliation:
The University, Gorakhpur, India

Extract

1. Introduction. In 1966, Kuttner(4) constructed (D, α) summability methods for functions. In this paper, strong and absolute summabilities based on (D, α) summability methods are defined and some of their properties investigated.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Borwein, D.On a scale of Abel type summability methods. Proc. Cambridge Philoa. Soc. 53 (1957), 318322.CrossRefGoogle Scholar
(2)Flett, T. M.On an extension of absolute summability and some theorems of Littlewood and Paley. Proc. London Math. Soc. (3) 7 (1957), 113141.Google Scholar
(3)Hyslop, J. M.Note on the strong summability of series. Proc. Glasgow Math. Assoc. 1 (1951/1953), 1620.CrossRefGoogle Scholar
(4)Kuttner, B.On ‘translated quasi-Cesàro’ summability. Proc. Cambridge Philos. Soc. 62 (1966), 705712.CrossRefGoogle Scholar
(5)Mishra, B. P.Strong summability of infinite series on a scale of Abel type summability methods. Proc. Cambridge Philos. Soc. 63 (1967), 119127.CrossRefGoogle Scholar
(6)Mishra, B. P.Absolute summability of infinite series on a scale of Abel type summability methods. Proc. Cambridge Philos. Soc. 64 (1968), 377387.CrossRefGoogle Scholar