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Year 2021, Volume: 70 Issue: 1, 320 - 330, 30.06.2021
https://doi.org/10.31801/cfsuasmas.729550

Abstract

References

  • Barnsley, M. F., Fractals Everywhere, Academic Press, Boston, MA, USA, 1988.
  • Barnsley, M. F., Superfractals, Cambridge University Press, New York, USA, 2006.
  • Burago, D., Burago, Y., Ivanov, S., A Course in Metric Geometry, AMS, San Diego, CA, USA, 2001.
  • Falconer, K. J., Fractal Geometry, Mathematical Foundations and Application, John Wiley, UK, 2014.
  • Hutchinson, J. E., Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), 713-747. http://dx.doi.org/10.1512/iumj.1981.30.30055.
  • Saltan, M., Özdemir, Y., Demir, B., An explicit formula of the intrinsic metric on the Sierpinski gasket via code representation, Turkish J. Math., 42(2) (2018), 716-725. http://doi.org/10.3906/mat-1702-55.
  • Saltan, M., Özdemir, Y., Demir, B., Geodecisc of the Sierpinski gasket, Fractals, 26(3) (2018), 1850024. https://doi.org/10.1142/S0218348X1850024X.
  • Williams, S. G., Symbolic dynamics and its applications, In Proceedings of Symposia in Applied Mathematics, AMS, 60 (2004), 1-11. https://doi.org/10.1090/psapm/060.

A metric formula on a quotient space which is related to the sequence space $\Sigma _{2}$

Year 2021, Volume: 70 Issue: 1, 320 - 330, 30.06.2021
https://doi.org/10.31801/cfsuasmas.729550

Abstract

In this paper, we first define an equivalence relation on the sequence space $\Sigma _{2}$. Then we equip the quotient set $\Sigma _{2}/_{\sim}$ with a metric $d_1$. We also determine an isometry map between the metric spaces $(\Sigma _{2}/_{\sim},d_1)$ and $([0,1],d_{eucl})$. Finally, we investigate the symmetry conditions with respect to some points on the metric space $(\Sigma _{2}/_{\sim},d_1)$ and we compare truncation errors for the computations which is obtained by the metrics $d_{eucl}$ and $d_1$.

References

  • Barnsley, M. F., Fractals Everywhere, Academic Press, Boston, MA, USA, 1988.
  • Barnsley, M. F., Superfractals, Cambridge University Press, New York, USA, 2006.
  • Burago, D., Burago, Y., Ivanov, S., A Course in Metric Geometry, AMS, San Diego, CA, USA, 2001.
  • Falconer, K. J., Fractal Geometry, Mathematical Foundations and Application, John Wiley, UK, 2014.
  • Hutchinson, J. E., Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), 713-747. http://dx.doi.org/10.1512/iumj.1981.30.30055.
  • Saltan, M., Özdemir, Y., Demir, B., An explicit formula of the intrinsic metric on the Sierpinski gasket via code representation, Turkish J. Math., 42(2) (2018), 716-725. http://doi.org/10.3906/mat-1702-55.
  • Saltan, M., Özdemir, Y., Demir, B., Geodecisc of the Sierpinski gasket, Fractals, 26(3) (2018), 1850024. https://doi.org/10.1142/S0218348X1850024X.
  • Williams, S. G., Symbolic dynamics and its applications, In Proceedings of Symposia in Applied Mathematics, AMS, 60 (2004), 1-11. https://doi.org/10.1090/psapm/060.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Mustafa Saltan 0000-0002-3252-3012

Nisa Aslan 0000-0002-2103-0511

Publication Date June 30, 2021
Submission Date April 29, 2020
Acceptance Date January 5, 2021
Published in Issue Year 2021 Volume: 70 Issue: 1

Cite

APA Saltan, M., & Aslan, N. (2021). A metric formula on a quotient space which is related to the sequence space $\Sigma _{2}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 320-330. https://doi.org/10.31801/cfsuasmas.729550
AMA Saltan M, Aslan N. A metric formula on a quotient space which is related to the sequence space $\Sigma _{2}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):320-330. doi:10.31801/cfsuasmas.729550
Chicago Saltan, Mustafa, and Nisa Aslan. “A Metric Formula on a Quotient Space Which Is Related to the Sequence Space $\Sigma _{2}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 1 (June 2021): 320-30. https://doi.org/10.31801/cfsuasmas.729550.
EndNote Saltan M, Aslan N (June 1, 2021) A metric formula on a quotient space which is related to the sequence space $\Sigma _{2}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 320–330.
IEEE M. Saltan and N. Aslan, “A metric formula on a quotient space which is related to the sequence space $\Sigma _{2}$”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 320–330, 2021, doi: 10.31801/cfsuasmas.729550.
ISNAD Saltan, Mustafa - Aslan, Nisa. “A Metric Formula on a Quotient Space Which Is Related to the Sequence Space $\Sigma _{2}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (June 2021), 320-330. https://doi.org/10.31801/cfsuasmas.729550.
JAMA Saltan M, Aslan N. A metric formula on a quotient space which is related to the sequence space $\Sigma _{2}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:320–330.
MLA Saltan, Mustafa and Nisa Aslan. “A Metric Formula on a Quotient Space Which Is Related to the Sequence Space $\Sigma _{2}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 1, 2021, pp. 320-3, doi:10.31801/cfsuasmas.729550.
Vancouver Saltan M, Aslan N. A metric formula on a quotient space which is related to the sequence space $\Sigma _{2}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):320-3.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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