Interpolation operators on a triangle with one curved side

We construct certain Lagrange, Hermite and Birkhoff-type operators, which interpolate a given function and some of its derivatives on the border of a triangle with one curved side, as well as some of their product and Boolean sum operators. We study the interpolation properties and the order of accuracy (degree of exactness and precision set) of the constructed operators, respectively the remainders of the corresponding interpolation formulas. Finally, we give some numerical examples.