| Title:
|
Translativity of absolute weighted mean summability (English) |
| Author:
|
Orhan, C. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
755-761 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we give necessary and sufficient conditions on $(p_n)$ for $| R,p_n| _k$, $k\ge 1$, to be translative. So we extend the known results of Al-Madi [1] and Cesco $\left[ 4\right] $ to the case $k>1$. (English) |
| MSC:
|
40A05 |
| MSC:
|
40F05 |
| MSC:
|
40G05 |
| idZBL:
|
Zbl 0949.40013 |
| idMR:
|
MR1658265 |
| . |
| Date available:
|
2009-09-24T10:18:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127452 |
| . |
| Reference:
|
[1] A. K. Al-Madi: On translativity of absolute weighted mean methods.Bull. Cal. Math. Soc. 79 (1987), 235–241. Zbl 0663.40003, MR 0943202 |
| Reference:
|
[2] W. Beekmann and K. Zeller: Theorie der Limitierungsverfahren.Springer-Verlag, Berlin-Heidelberg-New York, 1970. MR 0264267 |
| Reference:
|
[3] H. Bor: On the relative strength of two absolute summability methods.Proc. Amer. Math. Soc. 113 (1991), 1009–1012. Zbl 0743.40007, MR 1068115, 10.1090/S0002-9939-1991-1068115-X |
| Reference:
|
[4] R. P. Cesco: On the theory of linear transformations and the absolute summability of divergent series.Univ. Nac. La Plata. Publ. Fac. Cien. Fisicomat. Series 2, Revista 2 (1941), 147–156. MR 0007062 |
| Reference:
|
[5] G. G. Cooke: Infinite Matrices and Sequence Spaces.Macmillan Co., London, 1950. Zbl 0040.02501, MR 0040451 |
| Reference:
|
[6] J. A. Fridy: Abel transformations into $l^1$.Canad. Math. Bull. 25 (1982), 421–427. MR 0674557, 10.4153/CMB-1982-060-5 |
| Reference:
|
[7] B. Kuttner and B. Thorpe: Translativity of some absolute summability methods.Analysis 14 (1994), 57–65. MR 1280529, 10.1524/anly.1994.14.1.57 |
| Reference:
|
[8] F. M. Mears: Absolute regularity and Nörlund mean.Annals of Math. 38 (1937), 594–601. MR 1503356, 10.2307/1968603 |
| Reference:
|
[9] C. Orhan: On equivalence of summability methods.Math. Slovaca 40 (1990), 171–175. Zbl 0736.40002, MR 1094771 |
| Reference:
|
[10] R. E. Powell and S. M. Shah: Summability Theory and Applications.Prentice-Hall of India, New Delhi, 1988. |
| . |
