  We study approximation error bounds of isogeometric function spaces on a
specific type of singularly parameterized domains. In this context an
isogeometric function is the composition of a piecewise rational function with
the inverse of a piecewise rational geometry parameterization. We consider
domains where one edge of the parameter domain is mapped onto one point in
physical space. To be more precise, in our configuration the singular patch is
derived from a reparameterization of a regular triangular patch. On such a
domain one can define an isogeometric function space fulfilling certain
regularity criteria that guarantee optimal convergence. The main contribution
of this paper is to prove approximation error bounds for the previously defined
class of isogeometric discretizations.
