Some Estimates of the Maximum Modulus for Polynomials with Gaps
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 کاملSome compact generalization of inequalities for polynomials with prescribed zeros
Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$. In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$, $k^2 leq rRleq R^2$ and for $Rleq r leq k$. Our results refine and generalize certain well-known polynomial inequalities.
متن کاملHoradam Polynomials Estimates for $lambda$-Pseudo-Starlike Bi-Univalent Functions
In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coefficients of functions belongs to a new subclass of analytic and $lambda$-pseudo-starlike bi-univalent functions defined in the open unit disk $U$. Also, we discuss Fekete-Szeg$ddot{o}$ problem for functions belongs to this subclass.
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: 2019
ISSN: 1672-4070,1573-8175
DOI: 10.4208/ata.oa-2018-0017