| Title:
|
A class of statistical and $\sigma$-conservative matrices (English) |
| Author:
|
Çoşkun, Hüsamettin |
| Author:
|
Çakan, Celal |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
791-801 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In [5] and [10], statistical-conservative and $\sigma $-conservative matrices were characterized. In this note we have determined a class of statistical and $\sigma $-conservative matrices studying some inequalities which are analogous to Knopp’s Core Theorem. (English) |
| Keyword:
|
statistical convergence |
| Keyword:
|
invariant means |
| Keyword:
|
core theorems |
| Keyword:
|
matrix transformations |
| MSC:
|
40C05 |
| MSC:
|
40G99 |
| MSC:
|
40J05 |
| MSC:
|
46A45 |
| idZBL:
|
Zbl 1081.40003 |
| idMR:
|
MR2153102 |
| . |
| Date available:
|
2009-09-24T11:27:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128022 |
| . |
| Reference:
|
[1] H. Çoşkun, C. Çakan and Mursaleen: On the statistical and $\sigma $-cores.Studia Math. 153 (2003), 29–35. MR 1949047 |
| Reference:
|
[2] G. Das: Sublinear functionals and a class of conservative matrices.Bull. Inst. Math. Acad. Sinica 15 (1987), 89–106. Zbl 0632.46008, MR 0947779 |
| Reference:
|
[3] J. A. Fridy and C. Orhan: Statistical limit superior and limit inferior.Proc. Amer. Math. Soc. 125 (1997), 3625–3631. MR 1416085, 10.1090/S0002-9939-97-04000-8 |
| Reference:
|
[4] J. Li and J. A. Fridy: Matrix transformations of statistical cores of complex sequences.Analysis 20 (2000), 15–34. MR 1757066, 10.1524/anly.2000.20.1.15 |
| Reference:
|
[5] E. Kolk: Matrix maps into the space of statistically convergent bounded sequences.Proc. Estonian Acad. Sci. Phys. Math. 45 (1996), 187–192. Zbl 0865.40001, MR 1426169 |
| Reference:
|
[6] I. J. Maddox: Elements of Functional Analysis.Cambridge University Press, Cambridge, 1970. Zbl 0193.08601, MR 0390692 |
| Reference:
|
[7] S. L. Mishra, B. Satapathy and N. Rath: Invariant means and $\sigma $-core.J. Indian Math. Soc. 60 (1984), 151–158. MR 1292133 |
| Reference:
|
[8] Mursaleen: On some new invariant matrix methods of summability.Quart. J. Math. Oxford Ser. 2 34 (1983), 77–86. Zbl 0539.40006, MR 0688425, 10.1093/qmath/34.1.77 |
| Reference:
|
[9] R. Raimi: Invariant means and invariant matrix methods of summability.Duke Math. J. 30 (1963), 81–94. Zbl 0125.03201, MR 0154005, 10.1215/S0012-7094-63-03009-6 |
| Reference:
|
[10] P. Schaefer: Infinite matrices and invariant means.Proc. Amer. Math. Soc. 36 (1972), 104–110. Zbl 0255.40003, MR 0306763, 10.1090/S0002-9939-1972-0306763-0 |
| Reference:
|
[11] S. Simons: Banach limits, infinite matrices and sublinear functionals.J. Math. Anal. Appl. 26 (1969), 640–655. Zbl 0176.46001, MR 0241957, 10.1016/0022-247X(69)90203-0 |
| . |
