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2-Normlu Büyük Dizi Uzayları Üzerine Bir Not

Year 2022, Volume: 12 Issue: 1, 269 - 273, 15.06.2022
https://doi.org/10.31466/kfbd.1031895

Abstract

Bu çalışmada, (Gunawan, 2001) ve (Rafeiro et. al., 2018) çalışmalarindan esinlenerek 2-normlu büyük dizi uzaylarını tanımladık. Ayrıca, bu uzayların bazı temel özelliklerini verdik.

References

  • Duyar, C., Kanber, O. and Sağır, B., (2016). On n-normed Cesaro sequence space Cesn,p. Int. Electron. J. Pure Appl. Math., 10(2): 151-159.
  • Duyar, C., Sağır, B. and Oğur, O., (2017). On a class of n-normed double sequences related to p-summable double sequence space l_p^((2)). E. J. Mathematical Anal. App., 5(1): 106-111.
  • Gahler, S., (1964). Lineare 2-normierte Raume, Math. Nachr., 28: 1-43.
  • Gunawan, H., (2001). The space of p-summable sequences and its natural n-norm. Bull. Austral. Math. Soc., 64, 137-147.
  • Iwaniec, T. and Sbordone, C., (1992). On the integrability of the Jacobian under minimal hypotheses, Arch. Ration. Mech. Anal., 119(2), 129-143.
  • Jain, P. and Kumari, S., 2010. On grand Lorentz spaces and the maximal operator, Math. Student, 79.
  • Oğur, O., (2018). Superposition operator on some 2-normed sequence spaces. Karaelmas Science and Engineering journal, 8(1), 288-291.
  • Oğur, O., (2020). Grand Lorentz sequence space and its multiplication operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics , 69 (1) , 771-781.
  • Rafeiro, H., Samko, S. and Umarkhadzhiev, S., (2018). Grand Lebesgue sequence spaces. Georgian Math. J., 19(2), 235-246.
  • Samko, S. and Umarkhadzhiev, S., (2017), On grand Lebesgue spaces on sets of infinite measure, Math. Nachr., 290, 913-919.
  • Swe, T. T., (2019). Bounded linear 2-functionals in linear 2-normed space. Dagon University Commemoration of 25. Anniversary Silver Jubilee Research Journal, 9, 203.

A Note on 2-Normed Grand Sequence Spaces

Year 2022, Volume: 12 Issue: 1, 269 - 273, 15.06.2022
https://doi.org/10.31466/kfbd.1031895

Abstract

In this paper, we define 2-normed grand sequence space by inspiration of (Gunawan, 2001) and (Rafeiro et. al., 2018). Also, we give some basic properties of these spaces.

References

  • Duyar, C., Kanber, O. and Sağır, B., (2016). On n-normed Cesaro sequence space Cesn,p. Int. Electron. J. Pure Appl. Math., 10(2): 151-159.
  • Duyar, C., Sağır, B. and Oğur, O., (2017). On a class of n-normed double sequences related to p-summable double sequence space l_p^((2)). E. J. Mathematical Anal. App., 5(1): 106-111.
  • Gahler, S., (1964). Lineare 2-normierte Raume, Math. Nachr., 28: 1-43.
  • Gunawan, H., (2001). The space of p-summable sequences and its natural n-norm. Bull. Austral. Math. Soc., 64, 137-147.
  • Iwaniec, T. and Sbordone, C., (1992). On the integrability of the Jacobian under minimal hypotheses, Arch. Ration. Mech. Anal., 119(2), 129-143.
  • Jain, P. and Kumari, S., 2010. On grand Lorentz spaces and the maximal operator, Math. Student, 79.
  • Oğur, O., (2018). Superposition operator on some 2-normed sequence spaces. Karaelmas Science and Engineering journal, 8(1), 288-291.
  • Oğur, O., (2020). Grand Lorentz sequence space and its multiplication operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics , 69 (1) , 771-781.
  • Rafeiro, H., Samko, S. and Umarkhadzhiev, S., (2018). Grand Lebesgue sequence spaces. Georgian Math. J., 19(2), 235-246.
  • Samko, S. and Umarkhadzhiev, S., (2017), On grand Lebesgue spaces on sets of infinite measure, Math. Nachr., 290, 913-919.
  • Swe, T. T., (2019). Bounded linear 2-functionals in linear 2-normed space. Dagon University Commemoration of 25. Anniversary Silver Jubilee Research Journal, 9, 203.
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Oğuz Oğur 0000-0002-3206-5330

Early Pub Date June 15, 2022
Publication Date June 15, 2022
Published in Issue Year 2022 Volume: 12 Issue: 1

Cite

APA Oğur, O. (2022). A Note on 2-Normed Grand Sequence Spaces. Karadeniz Fen Bilimleri Dergisi, 12(1), 269-273. https://doi.org/10.31466/kfbd.1031895