  In this paper we prove an asymptotically sharp Bernstein-type inequality for
polynomials on analytic Jordan arcs. Also a general statement on mapping of a
domain bounded by finitely many Jordan curves onto a complement to a system of
the same number of arcs with rational function is presented here. This fact, as
well as, Borwein-Erd\'elyi inequality for derivative of rational functions on
the unit circle, Gonchar-Grigorjan estimate of the norm of holomorphic part of
meromorphic functions and Totik's construction of fast decreasing polynomials
play key roles in the proof of the main result.
