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

Mustafa Saltan; Nisa Aslan

doi:10.31801/cfsuasmas.729550

Araştırma Makalesi

Yıl 2021, Cilt: 70 Sayı: 1, 320 - 330, 30.06.2021

Mustafa Saltan Nisa Aslan

https://doi.org/10.31801/cfsuasmas.729550

Öz

Kaynakça

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 $\Sigma _{2}$

Yıl 2021, Cilt: 70 Sayı: 1, 320 - 330, 30.06.2021

Mustafa Saltan Nisa Aslan

https://doi.org/10.31801/cfsuasmas.729550

Öz

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 $d_1$.

Anahtar Kelimeler

Metric spaces, symbolic dynamics, isometry, symmetry, truncation errors

Kaynakça

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.

Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Research Article
Yazarlar	Mustafa Saltan 0000-0002-3252-3012 Nisa Aslan 0000-0002-2103-0511
Yayımlanma Tarihi	30 Haziran 2021
Gönderilme Tarihi	29 Nisan 2020
Kabul Tarihi	5 Ocak 2021
Yayımlandığı Sayı	Yıl 2021 Cilt: 70 Sayı: 1

Kaynak Göster

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. Haziran 2021;70(1):320-330. doi:10.31801/cfsuasmas.729550
Chicago	Saltan, Mustafa, ve 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, sy. 1 (Haziran 2021): 320-30. https://doi.org/10.31801/cfsuasmas.729550.
EndNote	Saltan M, Aslan N (01 Haziran 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 ve 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., c. 70, sy. 1, ss. 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 (Haziran 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 ve 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, c. 70, sy. 1, 2021, ss. 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.