Normed Gyrolinear Spaces: A Generalization of Normed Spaces Based on Gyrocommutative Gyrogroups

Document Type : Special Issue: AIMC 51


Niigata University, Japan


‎In this paper‎, ‎we consider a generalization of the real normed spaces and give some examples‎.


Main Subjects

1. T. Abe, O. Hatori, Generalized gyrovector spaces and a Mazur-Ulam theorem, Publ. Math. Debrecen 87 (2015) 393–413.

2. S. Kim, Distances of qubit density matrices on Bloch sphere,
J. Math. Phys. 52 (2011) 102303, 8 pp.

‎J. Lawson‎, ‎Y. Lim‎, Symmetric sets with midpoints and algebraically equivalent theories‎, Results Math. 46 (2004) 37-56‎.

4. A. A. Ungar,
Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces, Acad. Publ., Dordrecht, Kluwer, 2001.

5. A. A. Ungar,
Analytic Hyperbolic Geometry: Mathematical Foundations and Applications, World Scientific, Singapore, 2005.
6. ‎A. A. Ungar‎, Analytic Hyperbolic Geometry and Albert Einstein's ‎ Special Theory of Relativity, World Scientific Publishing Co‎. ‎Pte‎. ‎Ltd.‎, ‎ Hackensack‎, ‎NJ‎, 2008‎.

7. A. A. Ungar,
A Gyrovector Space Approach to Hyperbolic Geometry, Morgan & Claypool Pub., San Rafael, Californai, 2009.

8. A. A. Ungar,
Hyperbolic Triangle Centers: The Special Relativistic Approach, Springer-Verlag, New York, 2010.

‎A. A. Ungar‎,
Barycentric Calculus in Euclidean and Hyperbolic Geometry‎: A Comparative Introduction‎, World Scientific Publishing Co‎. ‎Pte‎. ‎Ltd.‎, ‎ Hackensack‎, ‎NJ‎, 2010.

‎A. A. Ungar‎,
Analytic Hyperbolic Geometry in n Dimensions‎: ‎An Introduction‎, CRC Press‎, ‎Boca Raton‎, ‎FL‎, 2015‎.