Certain Bernstein-type $

Certain Bernstein-type $L
Certain Bernstein-type $L_p$ inequalities for polynomials

Let $P(z)$ be a polynomial of degree $n,$ then it is known that for $αinmathbb{C}$ with $|α|leq frac{n}{2},$ begin{align*} underset{|z|=1}{max}|left|zP^{prime}(z)-αP(z)right|leq left|n-αright|underset{|z|=1}{max}|P(z)|. end{align*} This inequality includes Bernstein’s inequality, concerning the esti…