In this paper, we deal with a conjecture related to the images of ellipses (resp. circles) under similarities that are the special Möbius transformations. We consider ellipses (resp. circles) corresponding to any norm function (except in the Euclidean case) on the complex plane and examine some conditions to confirm this conjecture. Some illustrative examples are also given.
Möbius transformation, ellipse, norm
ÖZGÜR, NİHAL YILMAZ
"Ellipses and similarity transformations with norm functions,"
Turkish Journal of Mathematics: Vol. 42:
6, Article 30.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss6/30