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Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions on 2-Norm Space

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DOI: 10.4236/am.2014.516248    5,480 Downloads   5,972 Views  
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ABSTRACT

The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Aiyub, M. (2014) Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions on 2-Norm Space. Applied Mathematics, 5, 2602-2611. doi: 10.4236/am.2014.516248.

References

[1] Kizmaz, H. (1981) On Certain Sequence Spaces. Canadian Mathematical Bulletin, 24, 169-176.
http://dx.doi.org/10.4153/CMB-1981-027-5
[2] Et, M. and Çolak, R. (1995) On Some Generalized Difference Sequence Spaces. Soochow Journal of Mathematics, 21, 377-386.
[3] Et, M. and Esi, A. (2000) On K?the-Toeplitz Duals of Generalized Difference Sequence. Bulletin of the Malaysian Mathematical Society, 23, 25-32.
[4] Gahler, S. (1963) 2-Metrische Raume Undihre Topologishe Struktur. Mathematische Nachrichten, 26, 115-148.
http://dx.doi.org/10.1002/mana.19630260109
[5] Gunawan, H. and Mashadi, H. (2001) On Finite Dimensional 2-Normed Spaces. Soochow Journal of Mathematics, 27, 321-329.
[6] Freese, R.W. and Cho, Y.J. (2001) Geometry of Linear 2-Normed Spaces. Nova Science Publishers, Huntington.
[7] Gurdal, M. and Pehlivan, S. (2009) Statitical Convergence in 2-Normed Spaces. Southeast Asian Bulletin of Mathematics, 33, 257-264.
[8] Sahiner, A., Gurda, M., Saltan, S. and Gunawan, H. (2007) Ideal Convergence in 2-Normed Spaces. Taiwanese Journal of Mathematics, 11, 1477-1484.
[9] Schaefer, P. (1972) Infinite Matrices and Invariant Means. Proceedings of the American Mathematical Society, 36, 104-110.
http://dx.doi.org/10.1090/S0002-9939-1972-0306763-0
[10] Lorenz, G.G. (1948) A Contribution to the Theory of Divergent Sequences. Acta Mathematica, 80, 167-190.
http://dx.doi.org/10.1007/BF02393648
[11] Freedman, A.R., Sember, J.J. and Raphael, R. (1978) Some p-Cesáo-Type Summability Spaces. Proceedings of the London Mathematical Society, S3-37, 508-520.
http://dx.doi.org/10.1112/plms/s3-37.3.508
[12] Lindendstrauss, J. and Tzafriri, L. (1972) On Orlicz Sequence Spaces. Israel Journal of Mathematics, 10, 379-390.
http://dx.doi.org/10.1007/BF02771656
[13] Prashar, S.D. and Choudhry, B. (1995) Sequence Spaces Defined by Orlicz Functions. Indian Journal of Pure and Applied Mathematics, 25, 419-428.
[14] Maddox, I.J. (1976) Spaces of Strongly Summable Sequences. Quarterly Journal of Mathematics, 18, 345-355.
http://dx.doi.org/10.1093/qmath/18.1.345
[15] Tripathy, B.C., Et, M., Altin, Y. and Choudhry, B. (2003) On Some Class of Sequences Defined by Sequence of Orlicz Functions. Journal of Analysis and Applications, 1, 175-192.
[16] Tripathy, B.C. and Mohanta, S. (2004) On a Class of Generalized Lacunary Difference Sequence Spaces Defined by Orlicz Functions. Acta Mathematicae Applicatae Sinica, 20, 231-238.
http://dx.doi.org/10.1007/s10255-004-0163-1
[17] Tripathy, B.C., Mohanta, S. and Et, M. (2005) On Generalized Lacunary Difference Vector Valued Paranormed Sequences Defined by Orlicz Functions. International Journal of Mathematical Sciences, 4, 341-355.
[18] Maligranda, L. (1989) Orlicz Spaces and Interpolation, Seminars in Mathematics 5. Polish Academy of Science, Warsaw.
[19] Musielak, J. (1983) Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics, 1034.
[20] Kamthan, P.K. and Gupta, M. (1981) Sequence Spaces and Series. Marcel Dekker, Inc., New York.

  
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