Ellipses and similarity transformations with norm functions

Abstract

In this paper, we deal with a conjecture related to the images of ellipses (resp. circles) under similarities thatare the special Möbius transformations. We consider ellipses (resp. circles) corresponding to any norm function (exceptin the Euclidean case) on the complex plane and examine some conditions to confirm this conjecture. Some illustrativeexamples are also given.