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On new modular sequence space defined over 2-normed spaces

Year 2020, Volume: 22 Issue: 1, 248 - 254, 10.01.2020
https://doi.org/10.25092/baunfbed.680685

Abstract

In this paper, a new sequence space F(‖.,.‖,M,p,u) is defined by using a sequence of Orlicz functions in 2-normed spaces. Some various properties and some inclusions are also examined on this space.

References

  • Gähler, S., Uber 2-Banach räume, Mathematische Nachrichten, 42, 335-347, (1969).
  • Diminnie, C., Gähler, S. and White Jr. A.G., 2-inner product spaces, Demonstrario Mathematica, 6, 525-536, (1973).
  • White Jr. A.G., 2-Banach spaces, Mathematische Nachrichten, 42, 43-60, (1969).
  • Gähler, S., Siddiqi, A.H. and Gupta, S.C., Contributions to non-archimedean functional analysis, Mathematische Nachrichten, 69, 162-171, (1975).
  • Siddiqi, A.H., 2-normed spaces, The Aligarh Bulletin of Mathematics, 53-70, (1980).
  • Lindenstrauss, J., Tzafriri, L. On Orlicz sequence spaces, Israel Journal of Mathematics, 101, 379–390, (1971).
  • Gähler, S., Lineare 2-normierte Räume, Mathematische Nachrichten, 28, 1–43, (1965).
  • Maddox, I. J., Elements of functional analysis, Cambridge University Press, Cambridge, (1970).
  • Kamthan, P.K., Gupta, M., Sequence spaces and series, Marcel Dekker, New York, (1981).
  • Dutta, H., Kılıçman, A., Altun, Ö., Topological properties of some sequences defined over 2-normed spaces, SpringerPlus, 5, 2-16, (2016).
  • Dutta, H., Some statistically convergent difference sequence spaces defined over real 2-normed linear spaces, Applied Sciences, 12, 37–47, (2010).
  • Bektaş, Ç.A., Altin, Y., The sequence space l_M (p,q,s) on seminormed spaces, Indian Journal of Pure Applied Mathematics, 34(4), 529–534, (2003).
  • Rao, M.M., Ren, Z.D., Theory on Orlicz spaces, Marcel Dekker, New York, (1991).
  • Gürdal, M. and Şahiner, A., Ideal Convergence in n-normed spaces and some new sequence spaces via n-norm, Journal of Fundamental Sciences, 4(1), 233-244, (2008).
  • Şahiner, A., Gürdal, M., Saltan, S. and Gunawan, H., Ideal convergence in 2-normed spaces, Taiwanese Journal of Mathematics, 11(5), 1477-1484, (2007).
  • Şahiner, A. and Gürdal, M., New sequence spaces in n-normed spaces with respect to an Orlicz function, The Aligarh Bulletin of Mathematics, 27(1), 53-58, (2008).

2-normlu uzaylarda tanımlı yeni modular dizi uzayı

Year 2020, Volume: 22 Issue: 1, 248 - 254, 10.01.2020
https://doi.org/10.25092/baunfbed.680685

Abstract

Bu çalışmada, 2-normlu uzaylarda Orlicz fonksiyonlarının bir dizisi kullanılarak F(‖.,.‖,M,p,u) yeni dizi uzayı tanımlanmıştır. Ayrıca bu uzayın bazı özellikleri ve bazı kapsama bağıntıları incelenmiştir.

References

  • Gähler, S., Uber 2-Banach räume, Mathematische Nachrichten, 42, 335-347, (1969).
  • Diminnie, C., Gähler, S. and White Jr. A.G., 2-inner product spaces, Demonstrario Mathematica, 6, 525-536, (1973).
  • White Jr. A.G., 2-Banach spaces, Mathematische Nachrichten, 42, 43-60, (1969).
  • Gähler, S., Siddiqi, A.H. and Gupta, S.C., Contributions to non-archimedean functional analysis, Mathematische Nachrichten, 69, 162-171, (1975).
  • Siddiqi, A.H., 2-normed spaces, The Aligarh Bulletin of Mathematics, 53-70, (1980).
  • Lindenstrauss, J., Tzafriri, L. On Orlicz sequence spaces, Israel Journal of Mathematics, 101, 379–390, (1971).
  • Gähler, S., Lineare 2-normierte Räume, Mathematische Nachrichten, 28, 1–43, (1965).
  • Maddox, I. J., Elements of functional analysis, Cambridge University Press, Cambridge, (1970).
  • Kamthan, P.K., Gupta, M., Sequence spaces and series, Marcel Dekker, New York, (1981).
  • Dutta, H., Kılıçman, A., Altun, Ö., Topological properties of some sequences defined over 2-normed spaces, SpringerPlus, 5, 2-16, (2016).
  • Dutta, H., Some statistically convergent difference sequence spaces defined over real 2-normed linear spaces, Applied Sciences, 12, 37–47, (2010).
  • Bektaş, Ç.A., Altin, Y., The sequence space l_M (p,q,s) on seminormed spaces, Indian Journal of Pure Applied Mathematics, 34(4), 529–534, (2003).
  • Rao, M.M., Ren, Z.D., Theory on Orlicz spaces, Marcel Dekker, New York, (1991).
  • Gürdal, M. and Şahiner, A., Ideal Convergence in n-normed spaces and some new sequence spaces via n-norm, Journal of Fundamental Sciences, 4(1), 233-244, (2008).
  • Şahiner, A., Gürdal, M., Saltan, S. and Gunawan, H., Ideal convergence in 2-normed spaces, Taiwanese Journal of Mathematics, 11(5), 1477-1484, (2007).
  • Şahiner, A. and Gürdal, M., New sequence spaces in n-normed spaces with respect to an Orlicz function, The Aligarh Bulletin of Mathematics, 27(1), 53-58, (2008).
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Gülcan Atıci Turan 0000-0002-1009-6072

Publication Date January 10, 2020
Submission Date July 6, 2019
Published in Issue Year 2020 Volume: 22 Issue: 1

Cite

APA Atıci Turan, G. (2020). On new modular sequence space defined over 2-normed spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(1), 248-254. https://doi.org/10.25092/baunfbed.680685
AMA Atıci Turan G. On new modular sequence space defined over 2-normed spaces. BAUN Fen. Bil. Enst. Dergisi. January 2020;22(1):248-254. doi:10.25092/baunfbed.680685
Chicago Atıci Turan, Gülcan. “On New Modular Sequence Space Defined over 2-Normed Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, no. 1 (January 2020): 248-54. https://doi.org/10.25092/baunfbed.680685.
EndNote Atıci Turan G (January 1, 2020) On new modular sequence space defined over 2-normed spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 1 248–254.
IEEE G. Atıci Turan, “On new modular sequence space defined over 2-normed spaces”, BAUN Fen. Bil. Enst. Dergisi, vol. 22, no. 1, pp. 248–254, 2020, doi: 10.25092/baunfbed.680685.
ISNAD Atıci Turan, Gülcan. “On New Modular Sequence Space Defined over 2-Normed Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/1 (January 2020), 248-254. https://doi.org/10.25092/baunfbed.680685.
JAMA Atıci Turan G. On new modular sequence space defined over 2-normed spaces. BAUN Fen. Bil. Enst. Dergisi. 2020;22:248–254.
MLA Atıci Turan, Gülcan. “On New Modular Sequence Space Defined over 2-Normed Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, no. 1, 2020, pp. 248-54, doi:10.25092/baunfbed.680685.
Vancouver Atıci Turan G. On new modular sequence space defined over 2-normed spaces. BAUN Fen. Bil. Enst. Dergisi. 2020;22(1):248-54.