Title:
|
Banach and statistical cores of bounded sequences (English) |
Author:
|
Orhan, C. |
Author:
|
Yardimci, Ş. |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
54 |
Issue:
|
1 |
Year:
|
2004 |
Pages:
|
65-72 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper, we are mainly concerned with characterizing matrices that map every bounded sequence into one whose Banach core is a subset of the statistical core of the original sequence. (English) |
Keyword:
|
almost convergent sequence |
Keyword:
|
statistically convergent sequence |
Keyword:
|
core of a sequence |
MSC:
|
40A05 |
MSC:
|
40C05 |
idZBL:
|
Zbl 1045.40002 |
idMR:
|
MR2040219 |
. |
Date available:
|
2009-09-24T11:09:39Z |
Last updated:
|
2020-07-03 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127864 |
. |
Reference:
|
[1] B. Choudhary: An extension of Knopp’s Core Theorem.J. Math. Appl. 132 (1988), 226–233. Zbl 0648.40004, MR 0942366 |
Reference:
|
[2] J. Connor: The statistical and strong $p$-Cesáro convergences.Analysis 8 (1988), 47–63. MR 0954458, 10.1524/anly.1988.8.12.47 |
Reference:
|
[3] R. G. Cooke: Infinite Matrices and Sequence Spaces.Macmillan, , 1950. Zbl 0040.02501, MR 0040451 |
Reference:
|
[4] 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:
|
[5] G. Das and S. K. Mishra: A note on a theorem of Maddox on strong almost convergence.Math. Proc. Camb. Phil. Soc. 89 (1981), 393–396. MR 0602293, 10.1017/S0305004100058291 |
Reference:
|
[6] K. Demirci: A statistical core of a sequence.Demonstratio Math. 33 (2000), 343–353. Zbl 0959.40001, MR 1769428, 10.1515/dema-2000-0216 |
Reference:
|
[7] J. P. Duran: Infinite matrices and almost convergence.Math. Z. 128 (1972), 75–83. Zbl 0228.40005, MR 0340881, 10.1007/BF01111514 |
Reference:
|
[8] J. A. Fridy: On statistical convergence.Analysis 5 (1985), 301–313. Zbl 0588.40001, MR 0816582, 10.1524/anly.1985.5.4.301 |
Reference:
|
[9] J. A. Fridy: Statistical limit points.Proc. Amer. Math. Soc. 118 (1993), 1187–1192. Zbl 0776.40001, MR 1181163, 10.1090/S0002-9939-1993-1181163-6 |
Reference:
|
[10] 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:
|
[11] J. A. Fridy and C. Orhan: Statistical core theorems.J. Math. Anal. Appl. 208 (1997), 520–527. MR 1441452, 10.1006/jmaa.1997.5350 |
Reference:
|
[12] M. Jerison: The set of all generalized limits of bounded sequences.Canad. J. Math. 9 (1957), 79–89. Zbl 0077.31004, MR 0083697, 10.4153/CJM-1957-012-x |
Reference:
|
[13] J. P. King: Almost summable sequences.Proc. Amer. Math. Soc. 17 (1996), 1219–1225. MR 0201872 |
Reference:
|
[14] K. Knopp: Zur theorie der limitierungsverfahren (Erste Mitteilung).Math. Z. 31 (1930), 97–127. MR 1545100, 10.1007/BF01246399 |
Reference:
|
[15] E. Kolk: Matrix summability of statistically convergent sequences.Analysis 13 (1993), 77–83. Zbl 0801.40005, MR 1245744, 10.1524/anly.1993.13.12.77 |
Reference:
|
[16] 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:
|
[17] L. Loone: Knopp’s core and almost-convergence core in the space $m$.Tartu Riikl. All. Toimetised 335 (1975), 148–156. MR 0380356 |
Reference:
|
[18] G. G. Lorentz: A contribution to the theory of divergent sequences.Acta Math. 80 (1948), 167–190. Zbl 0031.29501, MR 0027868, 10.1007/BF02393648 |
Reference:
|
[19] I. J. Maddox: Some analogues of Knopp’s Core Theorem.Internat. J. Math. Math. Sci. 2 (1979), 605–614. Zbl 0416.40004, MR 0549529, 10.1155/S0161171279000454 |
Reference:
|
[20] H. I. Miller: A measure theoretical subsequence characterization of statistical convergence.Trans. Amer. Math. Soc. 347 (1995), 1811–1819. Zbl 0830.40002, MR 1260176, 10.1090/S0002-9947-1995-1260176-6 |
Reference:
|
[21] H. I. Miller and C. Orhan: On almost convergent and statistically convergent subsequences.Acta Math. Hungar. 93 (2001), 149–165. MR 1924673, 10.1023/A:1013877718406 |
Reference:
|
[22] I. Niven, H. S. Zuckerman and H. Montgomery: An Introduction to the Theory of Numbers, Fifth Ed.Wiley, New York, 1991. MR 1083765 |
Reference:
|
[23] C. Orhan: Sublinear functionals and Knopp’s Core Theorem.Internat. J. Math. Math. Sci. 13 (1990), 461–468. MR 1068009, 10.1155/S0161171290000680 |
Reference:
|
[24] G. M. Petersen: Regular Matrix Transformations.McGraw-Hill, London, 1966. Zbl 0159.35401, MR 0225045 |
Reference:
|
[25] T. Šalat: On statistically convergent sequences of real numbers.Math. Slovaca 30 (1980), 139–150. MR 0587239 |
Reference:
|
[26] 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 |
Reference:
|
[27] Ş. Yardimci: Core theorems for real bounded sequences.Indian J. Pure Appl. Math. 27 (1996), 861–867. Zbl 0862.40002, MR 1407221 |
. |