Some compact generalization of inequalities for polynomials with prescribed zeros
نویسندگان
چکیده مقاله:
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.
منابع مشابه
some 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 کاملSome Inequalities for Polynomials
Let pn(z) be a polynomial of degree n. Given that pn(z) has a zero on the circle \z\ = p(0 < p < oo) we estimate maxi , Ä>1 |/>„(z)| in terms of maxi:i , |/>„(z)|. We also consider some other related problems. It is well known (see [8, p. 346], or [6, vol. 1, p. 137, Problem III 269]) that if pn(z) = 2yt=oaAz/c 's a polynomial of degree « such that |p„(z)| â M for |z| Si 1, then at a point z ou...
متن کاملPolynomials with All Zeros Real and in a Prescribed Interval
We provide a characterization of the real-valued univariate polynomials that have only real zeros, all in a prescribed interval [a, b]. The conditions are stated in terms of positive semidefiniteness of related Hankel matrices.
متن کاملTurán Inequalities and Zeros of Orthogonal Polynomials∗
We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence pk+1 = xpk − ckpk−1, with a nondecreasing sequence {ck}. As a special case they include a non-asymptotic version of Máté, Nevai and Tot...
متن کاملTopics in polynomials - extremal problems, inequalities, zeros
Where you can find the topics in polynomials extremal problems inequalities zeros easily? Is it in the book store? On-line book store? are you sure? Keep in mind that you will find the book in this site. This book is very referred for you because it gives not only the experience but also lesson. The lessons are very valuable to serve for you, that's not about who are reading this topics in poly...
متن کاملInequalities for products of zeros of polynomials and entire functions
Estimates for products of the zeros of polynomials and entire functions are derived. By these estimates, new upper bounds for the counting function are suggested. In appropriate situations we improve the Jensen inequality for the counting functions and the Mignotte inequality for products of the zeros of polynomials. Mathematics subject classification (2010): 26C10, 30C15, 30D20.
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 43 شماره 1
صفحات 163- 170
تاریخ انتشار 2017-02-22
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023