Inequalities Concerning The Maximum Modulus of Polynomials
نویسندگان
چکیده
منابع مشابه
Some Inequalities concerning Derivative and Maximum Modulus of Polynomials
In this paper, we prove some compact generalizations of some well-known Bernstein type inequalities concerning the maximum modulus of a polynomial and its derivative in terms of maximum modulus of a polynomial on the unit circle. Besides, an inequality for self-inversive polynomials has also been obtained, which in particular gives some known inequalities for this class of polynomials. All the ...
متن کاملOn the Maximum Modulus of Polynomials. Ii
Let f(z) := ∑n ν=0 aνz ν be a polynomial of degree n having no zeros in the open unit disc, and suppose that max|z|=1 |f(z)| = 1. How small can max|z|=ρ |f(z)| be for any ρ ∈ [0 , 1)? This problem was considered and solved by Rivlin [4]. There are reasons to consider the same problem under the additional assumption that f ′(0) = 0. This was initiated by Govil [2] and followed up by the present ...
متن کاملSome Inequalities for Maximum Modules of Polynomials
A well-known result of Ankeney and Rivlin states that if p(z) is a polynomial of degree n, such that p(z) 0 in [z[ < 1, then maxlz[=R>_l Ip(z)l <_ (---)maxlzl= Ip(z)l. In this paper we 1)rove ,some generalizations and refinements of this result.
متن کاملextensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولInequalities 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Analysis in Theory and Applications
سال: 2018
ISSN: 1672-4070,1573-8175
DOI: 10.4208/ata.2018.v34.n2.7