Geodesic
Approximation of functions by polynomials with Hermitian interpolation and restrictions on the coefficients
Izvestiya. Mathematics , Tome 67 (2003) no. 1, pp. 183-206.

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We determine the order of approximation of real functions of finite smoothness by polynomials with various restrictions: approximation of functions and their derivatives with Hermitian interpolation at the endpoints, one-sided approximation (for example, from above), and assumptions on the coefficients. 
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R. M. Trigub. Approximation of functions by polynomials with Hermitian interpolation and restrictions on the coefficients. Izvestiya. Mathematics , Tome 67 (2003) no. 1, pp. 183-206. http://geodesic.mathdoc.fr/item/IM2_2003_67_1_a9/

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