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


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.

Share and Cite:

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.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Kizmaz, H. (1981) On Certain Sequence Spaces. Canadian Mathematical Bulletin, 24, 169-176.
[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.
[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.
[10] Lorenz, G.G. (1948) A Contribution to the Theory of Divergent Sequences. Acta Mathematica, 80, 167-190.
[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.
[12] Lindendstrauss, J. and Tzafriri, L. (1972) On Orlicz Sequence Spaces. Israel Journal of Mathematics, 10, 379-390.
[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.
[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.
[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.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.