Strong cyclic, parabolic and conical differentiability

Abstract

An arc A in the real inversive plane is strongly conformally differentiable at a point p of A if the circle through a fixed point different from p and two variable points of A converges as these points tend to p, and the circle through three points of A which tend to p converges. Analogous definitions of strong parabolic differentiability in the real affine plane, using parabolas and three conditions, and of strong conical differentiability in the real projective plane, using conies and four conditions, may be formulated.