Let ( ) := (1− 2 ) −1/2 and , be the ultraspherical polynomials with respect to ( ). Then, we denote the Stieltjes polynomials . In this paper, we consider the higher-order Hermite-Fejér interpolation operator +1, based on the zeros of , +1 and the higher order extended Hermite-Fejér interpolation operator H 2 +1, based on the zeros of , +1 , . When m is even, we show that Lebesgue constants of these interpolation operators are ( max{(1− ) −2,0} )(0 < < 1) and ( max{(1−2 ) −2,0} )(0 < < 1/2), respectively; that is, ‖H 2 +1, ‖ = ( max{(1−2 ) −2,0} )(0 < < 1) and ‖ +1, ‖ = ( max{(1− ) −2,0} )(0 < < 1/2). In the case of the Hermite-Fejér interpolation polynomials H 2 +1, [⋅] for 1/2 ≤ < 1, we can prove the weighted uniform convergence. In addition, when m is odd, we will show that these interpolations diverge for a certain continuous function on [−1, 1], proving that Lebesgue constants of these interpolation operators are similar or greater than log n
