Approximation of differentiable functions by algebraic polynomials (Q5920348)

The approximation of differentiable functions by algebraic polynomials is investigated. The uniform and integrals metrics are considered. It is shown that the structural characterization of continuous functions on \([-1,1]\) with a given order of the best approximation by algebraic polynomials depends on the points location on the interval. A number of the proper theorems is proved.