The best uniform polynomial approximation of the checkmark function f(x)=|x−α| is considered, as α varies in (−1,1). For each fixed degree n, minimax error En(α) shown to be piecewise analytic α. In addition, feature n−1 linear decreasing/increasing sections, called V-shapes. points alternation set are proven and monotone increasing their dynamics completely characterized. We also prove a conje...

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.

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.

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.