Markov-Bernstein-type inequalities for classes of polynomials with restricted zeros

We prove that an absolute constantc>0 exists such that$$|p'(y)| \leqslant c\min \left\{ {n(k + 1),\left( {\frac{{n(k + 1)}}{{1 - y^2 }}} \right)^{1/2} } \right\}\mathop {\max }\limits_{ - 1 \leqslant x \leqslant 1} |p(x)|, - 1 \leqslant y \leqslant 1,$$ for every real algebraic polynomial of degree at mostn having at mostk zeros in the open unit disk {z?C:|z|c, it is a sharp generalization of both Markov's and Bernstein's inequalities.