Some inequalities for maximum modulus of rational functions
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 کاملSome Integral Inequalities with Maximum of the Unknown Functions
This paper deals with a special type of delayed integral inequalities of Bihary type for scalar functions of two variables. The integrals involve the maximum of the unknown function over a past time interval. Several nonlinear types of integral inequalities are solved. The importance of these integral inequalities is based on their wide applications to the qualitative investigations of various ...
متن کاملSharp Estimates for the Maximum over Minimum Modulus of Rational Functions
Let m, n ≥ 0, λ > 1, and R be a rational function with numerator, denominator of degree ≤ m,n, respectively. In several applications, one needs to know the size of the set S ⊂ [0, 1] such that for r ∈ S, max |z|=r |R (z)| / min |z|=r |R (z)| ≤ λ. In an earlier paper, we showed that meas (S) ≥ 1 4 exp ( − 13 log λ ) , where meas denotes linear Lebesgue measure. Here we obtain, for each λ, the sh...
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 اولذخیره 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: Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
سال: 2019
ISSN: 2083-7402,0365-1029
DOI: 10.17951/a.2019.73.1.33-39