Banach and statistical cores of bounded sequences

Cihan Orhan; Şeyhmus Yardimci

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 1, page 65-72
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Orhan, Cihan, and Yardimci, Şeyhmus. "Banach and statistical cores of bounded sequences." Czechoslovak Mathematical Journal 54.1 (2004): 65-72. <http://eudml.org/doc/30837>.

@article{Orhan2004,
abstract = {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.},
author = {Orhan, Cihan, Yardimci, Şeyhmus},
journal = {Czechoslovak Mathematical Journal},
keywords = {almost convergent sequence; statistically convergent sequence; core of a sequence; almost convergent sequence; statistically convergent sequence; core of a sequence},
language = {eng},
number = {1},
pages = {65-72},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Banach and statistical cores of bounded sequences},
url = {http://eudml.org/doc/30837},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Orhan, Cihan
AU - Yardimci, Şeyhmus
TI - Banach and statistical cores of bounded sequences
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 65
EP - 72
AB - 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.
LA - eng
KW - almost convergent sequence; statistically convergent sequence; core of a sequence; almost convergent sequence; statistically convergent sequence; core of a sequence
UR - http://eudml.org/doc/30837
ER -

References

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  1. An extension of Knopp’s Core Theorem, J. Math. Appl. 132 (1988), 226–233. (1988) Zbl0648.40004MR0942366
  2. 10.1524/anly.1988.8.12.47, Analysis 8 (1988), 47–63. (1988) MR0954458DOI10.1524/anly.1988.8.12.47
  3. Infinite Matrices and Sequence Spaces, Macmillan, , 1950. (1950) Zbl0040.02501MR0040451
  4. Sublinear functionals and a class of conservative Matrices, Bull. Inst. Math. Acad. Sinica 15 (1987), 89–106. (1987) Zbl0632.46008MR0947779
  5. 10.1017/S0305004100058291, Math. Proc. Camb. Phil. Soc. 89 (1981), 393–396. (1981) MR0602293DOI10.1017/S0305004100058291
  6. 10.1515/dema-2000-0216, Demonstratio Math. 33 (2000), 343–353. (2000) Zbl0959.40001MR1769428DOI10.1515/dema-2000-0216
  7. 10.1007/BF01111514, Math. Z. 128 (1972), 75–83. (1972) Zbl0228.40005MR0340881DOI10.1007/BF01111514
  8. 10.1524/anly.1985.5.4.301, Analysis 5 (1985), 301–313. (1985) Zbl0588.40001MR0816582DOI10.1524/anly.1985.5.4.301
  9. 10.1090/S0002-9939-1993-1181163-6, Proc. Amer. Math. Soc. 118 (1993), 1187–1192. (1993) Zbl0776.40001MR1181163DOI10.1090/S0002-9939-1993-1181163-6
  10. 10.1090/S0002-9939-97-04000-8, Proc. Amer. Math. Soc. 125 (1997), 3625–3631. (1997) MR1416085DOI10.1090/S0002-9939-97-04000-8
  11. 10.1006/jmaa.1997.5350, J.  Math. Anal. Appl. 208 (1997), 520–527. (1997) MR1441452DOI10.1006/jmaa.1997.5350
  12. 10.4153/CJM-1957-012-x, Canad. J. Math. 9 (1957), 79–89. (1957) Zbl0077.31004MR0083697DOI10.4153/CJM-1957-012-x
  13. Almost summable sequences, Proc. Amer. Math. Soc. 17 (1996), 1219–1225. (1996) MR0201872
  14. 10.1007/BF01246399, Math. Z. 31 (1930), 97–127. (1930) MR1545100DOI10.1007/BF01246399
  15. 10.1524/anly.1993.13.12.77, Analysis 13 (1993), 77–83. (1993) Zbl0801.40005MR1245744DOI10.1524/anly.1993.13.12.77
  16. 10.1524/anly.2000.20.1.15, Analysis 20 (2000), 15–34. (2000) MR1757066DOI10.1524/anly.2000.20.1.15
  17. Knopp’s core and almost-convergence core in the space m , Tartu Riikl. All. Toimetised 335 (1975), 148–156. (1975) MR0380356
  18. 10.1007/BF02393648, Acta Math. 80 (1948), 167–190. (1948) Zbl0031.29501MR0027868DOI10.1007/BF02393648
  19. 10.1155/S0161171279000454, Internat. J.  Math. Math. Sci. 2 (1979), 605–614. (1979) Zbl0416.40004MR0549529DOI10.1155/S0161171279000454
  20. 10.1090/S0002-9947-1995-1260176-6, Trans. Amer. Math. Soc. 347 (1995), 1811–1819. (1995) Zbl0830.40002MR1260176DOI10.1090/S0002-9947-1995-1260176-6
  21. 10.1023/A:1013877718406, Acta Math. Hungar. 93 (2001), 149–165. (2001) MR1924673DOI10.1023/A:1013877718406
  22. An Introduction to the Theory of Numbers, Fifth Ed, Wiley, New York, 1991. (1991) MR1083765
  23. 10.1155/S0161171290000680, Internat. J.  Math. Math. Sci. 13 (1990), 461–468. (1990) MR1068009DOI10.1155/S0161171290000680
  24. Regular Matrix Transformations, McGraw-Hill, London, 1966. (1966) Zbl0159.35401MR0225045
  25. On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150. (1980) MR0587239
  26. 10.1016/0022-247X(69)90203-0, J.  Math. Anal. Appl. 26 (1969), 640–655. (1969) Zbl0176.46001MR0241957DOI10.1016/0022-247X(69)90203-0
  27. Core theorems for real bounded sequences, Indian J.  Pure Appl. Math. 27 (1996), 861–867. (1996) Zbl0862.40002MR1407221

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