  Let $\Gamma$ be a $C^{2+}$ Jordan arc and let $\Gamma_0$ be the open arc
which consists of interior points of $\Gamma$. We find concrete upper and lower
bounds for the limit of Widom factors for $L_2(\mu)$ extremal polynomials on
$\Gamma$ which was given in [18]. In addition, we show that the upper bound for
the limit supremum of Widom factors for the weighted Chebyshev polynomials
which was obtained in [18] can be improved once two normal derivatives of the
Green function do not agree at one point $z\in \Gamma_0$. We also show that if
$\Gamma_0$ is not analytic then we have improved upper bounds.

Classical Analysis and ODEs