The well-known inequality of P. Turán [Compos. Math. 7, 89-95 (1939; Zbl 0021.39504)] asserts that if \(P\) is an algebraic polynomial of degree at most \(n\) having all its zeros in \([-1,1]\), then \[ \| P'\| _\infty>\frac{\sqrt n}6\| P\| _\infty, \] where \(\| f\| _\infty:=\max\limits_{-1\leq t\leq 1}| f(t)| \). Here the constant \(\frac{\sqrt n}6\) is not best possible and Turán’s result was sharpened by J. Eröd [Mat. Fiz. Lapok 46, 58-83 (1939; Zbl 0021.39505)]. The paper under review is a survey on Turán type inequalities in the \(L^r\) norms. Most of them (in the \(L^2\) norm) were obtained by Professor A.K. Varma to memory of whom the above paper is dedicated.
For the entire collection see [Zbl 0890.00042].