A NOTE ON HERMITE-FEJ\'{E}R INTERPOLATION ON THE NON-UNIFORM NODES OF THE UNIT CIRCLE

This paper deals with the Hermite-Fej\'{e}r interpolation problem on the unit circle with the nodal system containing the vertically projected zeros of Jacobi's polynomial with boundary points on the unit circle. We worked upon three nodal structures throughout this paper and obtained rate of convergence for each case. Moreover, we did a comparison of all the three cases and provided some important conclusions.