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Polynomial operators for one-sided approximation to functions in $W^r_p [0,1]$. (English) Zbl 1258.41003
Some operators for one-sided approximation of differentiable functions by algebraic polynomials in $L_p$ spaces are presented. The estimates for the error of approximation are given with an explicit constant. The approximation of differentiable functions is considered in this paper. The approximation of nondifferentiable functions will be considered in another paper.

##### MSC:
 41A10 Approximation by polynomials 41A35 Approximation by operators (in particular, by integral operators)
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##### References:
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