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Monotone polynomial approximation in \(L^ p\). (English) Zbl 0688.41005

Summary: Jackson type estimates on the rate of approximation of monotone functions in \(L^ p[-1,1]\) by means of monotone polynomials are obtained. The estimates involve an \(L^ p\)-modulus of continuity or equivalently a Peetre functional that weights differently the behavior of the function in the middle of the interval and near the end points.

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
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