Some Extensions of the Markov Inequality for Polynomials

On a discrete norm for polynomials

“…This formula has been derived in previous work [2][3][4] and it has also been shown that n  j=0 |c n (j, θ )| ≤ n, 0 ≤ θ ≤ π .…”

“…Then, it has been established in [4] that (compare with (1.3)) so that we can restrict our attention to the range 0 ≤ θ ≤ π /2. We look for upper bounds for the terms in the last sum.…”

“…The famous inequality of Duffin and Schaeffer for the first derivative of polynomials in the interval [−1, 1] also follows from (1.9); see [4]. For matters concerning polynomial inequalities and interpolation formulae, we refer the reader to the book of Rahman and Schmeisser [5].…”