On the derivative and maximum modulus of a polynomial
نویسندگان
چکیده
منابع مشابه
On the Derivative and Maximum Modulus Ofa Polynomial
The above inequality, which is an immediate consequence of Bernstein’s inequality on the derivative of a trigonometric polynomial, is best possible with equality holding for the polynomial p(z)= λzn, λ being a complex number. If we restrict ourselves to the class of polynomials having no zeros in |z| < 1, then the above inequality can be sharpened. In fact Erdös conjectured and later Lax [7] pr...
متن کاملextensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولOn the polar derivative of a polynomial
For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...
متن کاملOn the maximum modulus of a polynomial and its derivatives
Let f (z) be an arbitrary entire function and M(f ,r) = max |z|=r | f (z)|. For a polynomial P(z) of degree n, having no zeros in |z| < k, k ≥ 1, Bidkham and Dewan (1992) proved max |z|=r |P (z)| ≤ (n(r + k) n−1 /(1 + k) n)max |z|=1 |P(z)| for 1 ≤ r ≤ k. In this paper, we generalize as well as improve upon the above inequality.
متن کاملInequalities for the Maximum Modulus of the Derivative of a Polynomial
Let P (z) be a polynomial of degree n and M(P, t) = Max|z|=t |P (z)|. In this paper we shall estimate M(P ′ , ρ) in terms of M(P, r) where P (z) does not vanish in the disk |z| ≤ K, K ≥ 1, 0 ≤ r < ρ < K and obtain an interesting refinement of some result of Dewan and Malik. We shall also obtain an interesting generalization as well as a refinement of well-known result of P. Turan for polynomial...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2006
ISSN: 1025-5834,1029-242X
DOI: 10.1155/jia/2006/54816