Derivatives of polynomials of best approximation

Behavior of Polynomials of Best Uniform Approximation

We investigate the asymptotic behavior of the polynomials {Pn(f)}'t' of best uniform approximation to a function f that is continuous on a compact set K of the complex plane C and analytic in the interior of K, where K has connected complement. For example, we show that for "most" functions f, the error f -Pn(f) does not decrease faster at interior points of K than on K itself. We also describe...

On Polynomials of Best One Sided Approximation

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Generalized Derivatives and Approximation by Polynomials*

Best one-sided approximation of polynomials under L1 norm

In this paper, we develop an analytic solution for the best one-sided approximation of polynomials under L1 norm, that is, we 0nd two polynomials with lower degree which bound the given polynomial such that the areas between the bounding polynomials and the given polynomial attain minimum. The key ingredient of our technique is a characterization for one-sided approximations based on orthogonal...

Best Approximation in TVS

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.