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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 70 Issue: 1

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

Mustafa Saltan(ESKISEHIR TECHNICAL UNIVERSİTY)0000-0002-3252-3012
Nisa Aslan(ESKISEHIR TECHNICAL UNIVERSİTY)0000-0002-2103-0511
Sayfa
—
Yayın Tarihi
2021-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 $d_1$.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we first define an equivalence relation on the sequence space $\Sigma _{2}$.
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Temel Bulgular & Veri:Then we equip the quotient set $\Sigma _{2}/_{\sim}$ with a metric $d_1$.
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Sonuç & Katkı: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 $d_1$.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Metric spaces · symbolic dynamics · isometry

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 $d_1$.

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Bu Makaleye Atıf Yap

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, Volume: 70 Issue: 1. https://doi.org/10.31801/cfsuasmas.729550

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Kaynakça (8)

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  4. Falconer, K. J., Fractal Geometry, Mathematical Foundations and Application, John Wiley, UK, 2014.
  5. 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.
  6. 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.
  7. Saltan, M., Özdemir, Y., Demir, B., Geodecisc of the Sierpinski gasket, Fractals, 26(3) (2018), 1850024. https://doi.org/10.1142/S0218348X1850024X.
  8. 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.