On restricted derivative approximation
Compositio Mathematica, Tome 74 (1990) no. 3, pp. 327-331. 
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     author = {Yang, Zi-Xiao and Li, Bu-Xi},
     title = {On restricted derivative approximation},
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     publisher = {Kluwer Academic Publishers},
     volume = {74},
     number = {3},
     year = {1990},
     mrnumber = {1055699},
     zbl = {0697.41002},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1990__74_3_327_0/}
}
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Yang, Zi-Xiao; Li, Bu-Xi. On restricted derivative approximation. Compositio Mathematica, Tome 74 (1990) no. 3, pp. 327-331. http://archive.numdam.org/item/CM_1990__74_3_327_0/

[1] Roulier, J.A., Best Approximation to Functions with Restricted derivate, J. Approximation Theory 17 (1976), 344-347. | MR | Zbl

[2] Feinerman, R.P. and Newman, D.J., "Polynomial Approximation", Williams and Wilkins, Baltimore 1974. | MR | Zbl

[3] Leviatan, D., The behavior of the derivatives of the algebraic polynomials of best approximation, J. Approximation Theory 35 (1982), 169-176. | MR | Zbl