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Journal of Mathematics and Applications

Journal of Mathematics and Applications
10/38, DOI: 10.7862/rf.2015.10

Some seminormed difference sequence spaces defined by a Musielak-Orlicz function over n-normed spaces

K. Raj, S. K. Sharma

DOI: 10.7862/rf.2015.10

Abstract

 In the present paper we introduced some seminormed difference sequence spaces combining lacunary sequences and Musielak-Orlicz function M = (Mk) over n-normed spaces and examine some topological properties and inclusion relations between resulting sequence spaces.

 

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References

  1. A. Esi, Some new paranormed sequence spaces defined by Orlicz function, International Journal of Science, Environment and Technology, 1 (2012), 49-55.
  2. A. Esi, Strongly lacunary summable double sequence spaces in n-normed spaces defined by ideal convergence and an Orlicz function, Advanced Modeling and Optimization, 14 (2012), 79-86.
  3. A. Esi, Strongly almost summable sequence spaces in 2-normed spaces defined by ideal convergence and an Orlicz function, Stud. Univ. Babes-Bolyai Math. 57 (2012), 75-82.
  4.  M. Et and R. C¸olak, On some generalized difference sequence spaces, Soochow. J. Math., 21 (1995), 377-386.
  5. A. R. Freedman, J. J. Sember and M. Raphael, Some Cesaro-type summability spaces, Proc. London Math. Soc., 37 (1978), 508-520.
  6. S. Gahler, Linear 2-normietre Rume, Math. Nachr., 28 (1965), 1-43.
  7. H. Gunawan, On n-inner product, n-norms, and the Cauchy-Schwartz inequality, Sci. Math. Jpn., 5 (2001), 47-54.
  8. H. Gunawan, The space of p-summable sequence and its natural n-norm, Bull. Aust. Math. Soc., 64 (2001), 137-147.
  9. H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (2001), 631-639.
  10. M. Gungor and M. Et, ∆r-strongly almost summable sequences defined by Orlicz functions, Indian J. Pure Appl. Math., 34 (2003), 1141-1151.
  11. H. Kızmaz, On certain sequence spaces, Canad. Math-Bull., 24 (1981), 169-176.
  12. J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 345-355.
  13. G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Mathematica, 80 (1948), 167-190.
  14. I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math., 18 (1967), 345-355.
  15. I. J. Maddox, A new type of convergence, Math. Proc. Camb. Phil. Soc., 83 (1978), 61-64.
  16. L. Maligranda, Orlicz spaces and interpolation, Seminars in Mathematics 5, Polish Academy of Science, 1989.
  17. A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299-319.
  18. M. Mursaleen, On statistical convergence in random 2-normed spaces, Acta Sci. Math. (szeged), 76 (2010), 101–109.
  19. M. Mursaleen and A. Alotaibi, On I-convergence in random 2-normed spaces, Math. Slovaca, 61 (2011), 933–940.
  20. J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034 (1983).
  21. K. Raj and S. K. Sharma, Some sequence spaces in 2-normed spaces defined by Musielak-Orlicz function, Acta Univ. Sapientiae Math., 3 (2011), 97-109.
  22. K. Raj and S. K. Sharma, Some generalized difference double sequence spaces defined by a sequence of Orlicz-function, Cubo, 14 (2012), 167-189.
  23. K. Raj and S. K. Sharma, Some multiplier sequence spaces defined by a MusielakOrlicz function in n-normed spaces, New Zealand J. Math., 42 (2012), 45-56.
  24. E. Savas, Some sequence spaces defined by Orlicz functions, Arch. Math., 40 (2004), 33–40.
  25. E. Savas, Some new double sequence spaces defined by Orlicz function in nnormed space, Journal of Inequalities and Applications, Vol (2011), ID 592840, 1–9.
  26. A. Wilansky, summability through Functional Analysis, North- Holland Math. Stud. 85 (1984)

About this Article

TITLE:
Some seminormed difference sequence spaces defined by a Musielak-Orlicz function over n-normed spaces

AUTHORS:
K. Raj (1)
S. K. Sharma (2)

AUTHORS AFFILIATIONS:
(1) School of Mathematics Shri Mata Vaishno Devi University Katra-182320, J&K, Indii
(2) Department of mathematics Model Institute of Engineering & Technology Kot Bhalwal-181122, J&K, INDIA

JOURNAL:
Journal of Mathematics and Applications
10/38

KEY WORDS AND PHRASES:
Paranorm space, Difference sequence spaces, Orlicz function, Musielak-Orlicz function, n-normed spaces

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/38

DOI:
10.7862/rf.2015.10

URL:
http://dx.doi.org/10.7862/rf.2015.10

RECEIVED:
2014-09-19

COPYRIGHT:
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