Is There Any Metric Line Which Can Be Represented By A Single Fixed Point?

Oğuzhan Demirel

doi:10.33484/sinopfbd.469669

Is There Any Metric Line Which Can Be Represented By A Single Fixed Point?

Abstract

In this paper, determining metric lines in Levenberg plane, a special metric line example which can be written by using a single fixed point is presented. Moreover, we prove nonexistence of periodic lines in Levenberg plane and give a problem whether there exist a distance space in which periodic lines written by using a single fixed point?

Keywords

Metric spaces,functional equations of metric and periodic lines and their solutions,Levenberg plane

References

[1] Benz, W., Metric and periodic lines in real inner product space geometries. Monatsh. Math.141 (2004), no. 1, 1–10.
[2] Benz, W., Classical Geometries in Modern Contexts, Birkhauser, 2007.
[3] Blumenthal LM, Menger K (1970) Studies in Geometry. San Francisco: Freeman.
[4] Demirel, O., Seyrantepe E.S, Sönmez, N., Metric and periodic lines in the Poincare ball modelof hyperbolic geometry, Bull. Iran. Math. Soc. 38 (2012), no. 3, 805–815.
[5] Demirel, O., Seyrantepe E.S, The cogyrolines of Möbius gyrovector spaces are metric but notperiodic, Aequationes Math. 85 (2013), no. 1-2, 185–200.
[6] Gelisgen, O., On the Congruence of Triangles in Levenberg Plane, Dumlupinar ¨ Universitesi ¨Fen Bilimleri Enstitüsü 14, 2007.
[7] Höfer, R., Metric lines in Lorentz-Minkowski geometry, Aequationes Math. 71 (2006), no. 1-2,162–173.
[8] Höfer, R., Metric and Periodic lines in de Sitter’s World, J.Geom. 90 (2008), 66–82.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Oğuzhan Demirel ^*
Türkiye

Publication Date

June 27, 2019

Submission Date

October 11, 2018

Acceptance Date

March 8, 2019

Published in Issue

Year 2019 Volume: 4 Number: 1

DOI

https://doi.org/10.33484/sinopfbd.469669

IZ

https://izlik.org/JA49KN33PX

Cite

RIS / Bibtex

APA

Demirel, O. (2019). Is There Any Metric Line Which Can Be Represented By A Single Fixed Point? Sinop Üniversitesi Fen Bilimleri Dergisi, 4(1), 54-62. https://doi.org/10.33484/sinopfbd.469669

AMA

1.Demirel O. Is There Any Metric Line Which Can Be Represented By A Single Fixed Point? Sinop Uni J Nat Sci. 2019;4(1):54-62. doi:10.33484/sinopfbd.469669

Chicago

Demirel, Oğuzhan. 2019. “Is There Any Metric Line Which Can Be Represented By A Single Fixed Point?”. Sinop Üniversitesi Fen Bilimleri Dergisi 4 (1): 54-62. https://doi.org/10.33484/sinopfbd.469669.

EndNote

Demirel O (June 1, 2019) Is There Any Metric Line Which Can Be Represented By A Single Fixed Point? Sinop Üniversitesi Fen Bilimleri Dergisi 4 1 54–62.

IEEE

[1]O. Demirel, “Is There Any Metric Line Which Can Be Represented By A Single Fixed Point?”, Sinop Uni J Nat Sci, vol. 4, no. 1, pp. 54–62, June 2019, doi: 10.33484/sinopfbd.469669.

ISNAD

Demirel, Oğuzhan. “Is There Any Metric Line Which Can Be Represented By A Single Fixed Point?”. Sinop Üniversitesi Fen Bilimleri Dergisi 4/1 (June 1, 2019): 54-62. https://doi.org/10.33484/sinopfbd.469669.

JAMA

1.Demirel O. Is There Any Metric Line Which Can Be Represented By A Single Fixed Point? Sinop Uni J Nat Sci. 2019;4:54–62.

MLA

Demirel, Oğuzhan. “Is There Any Metric Line Which Can Be Represented By A Single Fixed Point?”. Sinop Üniversitesi Fen Bilimleri Dergisi, vol. 4, no. 1, June 2019, pp. 54-62, doi:10.33484/sinopfbd.469669.

Vancouver

1.Oğuzhan Demirel. Is There Any Metric Line Which Can Be Represented By A Single Fixed Point? Sinop Uni J Nat Sci. 2019 Jun. 1;4(1):54-62. doi:10.33484/sinopfbd.469669