On the analogue of a de la Vallée Poussin's problem for arcs in the complex plane (Q1821904)

Let \(z_ 1z_ 2\) be a Jordan arc with end points \(z_ 1\) and \(z_ 2\) and \(z_ 0\), \(z_ 0\neq z_ 1,z_ 2\) \(z_ 0\in z_ 1z_ 2\) and \[ f(z)= \begin{cases} z-z_ 0, &z\in z_ 1z_ 0 \\ z_ 0-z, &z\in z_ 0z_ 2. \end{cases} \] The exact estimation of the best polynomial approximation of f on \(z_ 1z_ 2\) is found in terms of the Riemann mapping function of \({\bar {\mathbb{C}}}\setminus z_ 1z_ 2\) onto \(| w| >1\).