Some sequence spaces defined by Orlicz functions

Ekrem Savaş; Rahmet Savaş

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 1, page 33-40
  • ISSN: 0044-8753

Abstract

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In this paper we introduce a new concept of λ -strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. It is also shown that if a sequence is λ -strongly convergent with respect to an Orlicz function then it is λ -statistically convergent.

How to cite

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Savaş, Ekrem, and Savaş, Rahmet. "Some sequence spaces defined by Orlicz functions." Archivum Mathematicum 040.1 (2004): 33-40. <http://eudml.org/doc/249299>.

@article{Savaş2004,
abstract = {In this paper we introduce a new concept of $\lambda $-strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. It is also shown that if a sequence is $\lambda $-strongly convergent with respect to an Orlicz function then it is $\lambda $-statistically convergent.},
author = {Savaş, Ekrem, Savaş, Rahmet},
journal = {Archivum Mathematicum},
keywords = {sequence spaces; Orlicz function; de la Vallée-Poussin means; de la Valée-Poussin means},
language = {eng},
number = {1},
pages = {33-40},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some sequence spaces defined by Orlicz functions},
url = {http://eudml.org/doc/249299},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Savaş, Ekrem
AU - Savaş, Rahmet
TI - Some sequence spaces defined by Orlicz functions
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 1
SP - 33
EP - 40
AB - In this paper we introduce a new concept of $\lambda $-strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. It is also shown that if a sequence is $\lambda $-strongly convergent with respect to an Orlicz function then it is $\lambda $-statistically convergent.
LA - eng
KW - sequence spaces; Orlicz function; de la Vallée-Poussin means; de la Valée-Poussin means
UR - http://eudml.org/doc/249299
ER -

References

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  6. Maddox I. J., Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc. 100 (1986), 161–166. (1986) Zbl0631.46010MR0838663
  7. Mursaleen, λ -statistical convergence, Math. Slovaca 50, No.1 (2000), 111–115. Zbl0953.40002MR1764349
  8. Nakano H., Concave modulus, J. Math. Soc. Japan 5 (1953), 29–49. (1953) MR0058882
  9. Parashar S. D., Choudhary B., Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math. 25 (14) (1994), 419–428. (1994) Zbl0802.46020MR1272814
  10. Ruckle W. H., FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25 (1973), 973–978. (1973) Zbl0267.46008MR0338731
  11. Savaş E., Strongly almost convergent sequences defined by Orlicz functions, Comm. Appl. Anal. 4 (2000), 453–458. Zbl1084.46513MR1843760
  12. Savaş E., Strong almost convergence and almost λ -statistical convergence, Hokkaido Math. J. 24(3), (2000), 531–536. Zbl0963.40001MR1795490
  13. Savaş E., Rhoades B. E., On some new sequence spaces of invariant means defined by Orlicz functions, Math. Inequal. Appl. 5(2) (2002), 271–281. Zbl1010.46006MR1899095
  14. Wilansky A., Summability through Functional Analysis, North-Holland Math. Stud. 85 (1984). (1984) Zbl0531.40008MR0738632

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