Bernstein-type inequalities for the derivatives of constrained polynomials. (English) Zbl 0753.41011
Using Lorentz representation and a Markov-type inequality for the derivative of Müntz polynomials due to D. Newman, the author in this paper provides a short proof of a theorem of P. Borwein [Proc. Am. Math. Soc. 93, 43-47 (1985; Zbl 0564.26003)]. Also using the same method he proves a sharp Bernstein-type inequality for another family of classes of constrained polynomials.
Reviewer: S.M.Mazhar (Kuwait)
MSC:
| 41A17 | Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) |
| 26C05 | Real polynomials: analytic properties, etc. |
| 26C10 | Real polynomials: location of zeros |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
