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This paper deals with the Hermite-Fej´er 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.

This paper deals with the Hermite-Fejér 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.

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