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SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES

Year 2015, Volume: 3 Issue: 1, 16 - 28, 01.04.2015

Abstract

In this paper we present new classes of sequence spaces using la- cunary sequences and a Musielak-Orlicz function over n-normed spaces. We examine some topological properties and prove some interesting inclusion re- lations between them.

References

  • [1] A.Esi, Some new paranormed sequence spaces de ned 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 de ned 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 de ned by ideal convergence and an Orlicz function, Stud. Univ. Babes-Bolyai Math. 57 (2012), 75-82.
  • [4] A. R. Freedman, J. J. Sember and M. Raphael, Some Cesaro-type summability spaces, Proc. London Math. Soc., 37 (1978), 508-520. [5] S. Gahler, Linear 2-normietre Rume, Math. Nachr., 28 (1965), 1-43.
  • [6] H. Gunawan, On n-inner product, n-norms, and the Cauchy-Schwartz inequality, Sci. Math. Jap., 5 (2001), 47-54.
  • [7] H. Gunawan, The space of p-summable sequence and its natural n-norm, Bull. Aust. Math. Soc., 64 (2001), 137-147.
  • [8] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (2001), 631-639.
  • [9] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Mathematica, 80 (1948), 167-190.
  • [10] Lindenstrauss, J. and Tzafriri, L., On Orlicz sequence spaces, Israel J. Math., 10 (1971), 345-355.
  • [11] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math., 18 (1967), 345-355.
  • [12] I. J. Maddox, A new type of convergence, Math. Proc. Camb. Phil. Soc., 83 (1978), 61-64.
  • [13] L. Maligranda, Orlicz spaces and interpolation, Seminars in Mathematics 5, Polish Academy of Science, 1989.
  • [14] A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299-319.
  • [15] M. Mursaleen and A. K. Noman, On some new sequence spaces of non absolute type related to the spaces lp and l1 I, Filomat, 25 (2011), 33-51.
  • [16] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034 (1983).
  • [17] K. Raj, A. K. Sharma and S. K. Sharma, A Sequence space de ned by a Musielak-Orlicz function, Int. J. Pure Appl. Math., 67(2011), 475-484.
  • [18] K. Raj and S. K. Sharma, Some sequence spaces in 2-normed spaces de ned by Musielak- Orlicz functions, Acta Univ. Sapientiae Math., 3 (2011), 97-109.
  • [19] A. Wilansky, summability through Functional Analysis, North- Holland Math. stud. 85(1984).
Year 2015, Volume: 3 Issue: 1, 16 - 28, 01.04.2015

Abstract

References

  • [1] A.Esi, Some new paranormed sequence spaces de ned 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 de ned 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 de ned by ideal convergence and an Orlicz function, Stud. Univ. Babes-Bolyai Math. 57 (2012), 75-82.
  • [4] A. R. Freedman, J. J. Sember and M. Raphael, Some Cesaro-type summability spaces, Proc. London Math. Soc., 37 (1978), 508-520. [5] S. Gahler, Linear 2-normietre Rume, Math. Nachr., 28 (1965), 1-43.
  • [6] H. Gunawan, On n-inner product, n-norms, and the Cauchy-Schwartz inequality, Sci. Math. Jap., 5 (2001), 47-54.
  • [7] H. Gunawan, The space of p-summable sequence and its natural n-norm, Bull. Aust. Math. Soc., 64 (2001), 137-147.
  • [8] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (2001), 631-639.
  • [9] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Mathematica, 80 (1948), 167-190.
  • [10] Lindenstrauss, J. and Tzafriri, L., On Orlicz sequence spaces, Israel J. Math., 10 (1971), 345-355.
  • [11] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math., 18 (1967), 345-355.
  • [12] I. J. Maddox, A new type of convergence, Math. Proc. Camb. Phil. Soc., 83 (1978), 61-64.
  • [13] L. Maligranda, Orlicz spaces and interpolation, Seminars in Mathematics 5, Polish Academy of Science, 1989.
  • [14] A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299-319.
  • [15] M. Mursaleen and A. K. Noman, On some new sequence spaces of non absolute type related to the spaces lp and l1 I, Filomat, 25 (2011), 33-51.
  • [16] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034 (1983).
  • [17] K. Raj, A. K. Sharma and S. K. Sharma, A Sequence space de ned by a Musielak-Orlicz function, Int. J. Pure Appl. Math., 67(2011), 475-484.
  • [18] K. Raj and S. K. Sharma, Some sequence spaces in 2-normed spaces de ned by Musielak- Orlicz functions, Acta Univ. Sapientiae Math., 3 (2011), 97-109.
  • [19] A. Wilansky, summability through Functional Analysis, North- Holland Math. stud. 85(1984).
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ayhan Eşi

S. K. Sharma This is me

Publication Date April 1, 2015
Submission Date June 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Eşi, A., & Sharma, S. K. (2015). SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES. Konuralp Journal of Mathematics, 3(1), 16-28.
AMA Eşi A, Sharma SK. SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES. Konuralp J. Math. April 2015;3(1):16-28.
Chicago Eşi, Ayhan, and S. K. Sharma. “SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES”. Konuralp Journal of Mathematics 3, no. 1 (April 2015): 16-28.
EndNote Eşi A, Sharma SK (April 1, 2015) SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES. Konuralp Journal of Mathematics 3 1 16–28.
IEEE A. Eşi and S. K. Sharma, “SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES”, Konuralp J. Math., vol. 3, no. 1, pp. 16–28, 2015.
ISNAD Eşi, Ayhan - Sharma, S. K. “SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES”. Konuralp Journal of Mathematics 3/1 (April 2015), 16-28.
JAMA Eşi A, Sharma SK. SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES. Konuralp J. Math. 2015;3:16–28.
MLA Eşi, Ayhan and S. K. Sharma. “SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES”. Konuralp Journal of Mathematics, vol. 3, no. 1, 2015, pp. 16-28.
Vancouver Eşi A, Sharma SK. SOME PARANORMED SEQUENCE SPACES DEFINED BY A MUSIELAK-ORLICZ FUNCTION OVER N-NORMED SPACES. Konuralp J. Math. 2015;3(1):16-28.
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