  The aim of this paper is to study the approximation of functions using a
higher order Hermite-Fejer interpolation process on the unit circle. The system
of nodes is composed of vertically projected zeros of Jacobi polynomials onto
the unit circle with boundary points at $ \pm1 $. Values of the polynomial and
its first four derivatives are fixed by the interpolation conditions at the
nodes. Convergence of the process is obtained for analytic functions on a
suitable domain, and the rate of convergence is estimated.
