Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Gulzar, Suhail"'
If all the zeros of $n$th degree polynomials $f(z)$ and $g(z) = \sum_{k=0}^{n}\lambda_k\binom{n}{k}z^k$ respectively lie in the cricular regions $|z|\leq r$ and $|z| \leq s|z-\sigma|$, $s>0$, then it was proved by Marden \cite[p. 86]{mm} that all the
Externí odkaz:
http://arxiv.org/abs/2412.01088
If $P(z)=\sum_{j=0}^{n}a_jz^j$ is a polynomial of degree $n$ having no zero in $|z|<1,$ then it was recently proved that for every $p\in[0,+\infty]$ and $s=0,1,\ldots,n-1,$ \begin{align*} \left\|a_nz+\frac{a_s}{\binom{n}{s}}\right\|_{p}\leq \frac{\le
Externí odkaz:
http://arxiv.org/abs/2411.19831
Autor:
Rather, N. A., Gulzar, Suhail
Recently GM Sofi & SA Shabir [arXive: 1903.01850v2 [math.GM] 6 Mar 2019] made an attempt to prove the Sendov's conjecture. But unfortunately the proof is not correct. In this note, we discuss the fallacy in the proof.
Externí odkaz:
http://arxiv.org/abs/1903.04026
Publikováno v:
Acta Universitatis Sapientiae: Mathematica, Vol 14, Iss 2, Pp 211-219 (2022)
According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central importance in the geometry of critical points in the analytic theory of polynomials. In this
Externí odkaz:
https://doaj.org/article/4ea278d84ad54f7dae3f6f4db009ef2e
In this paper we obtain some refinements of a well-known result of Enestr\"o-Kakeya concerning the bounds for the moduli of the zeros of polynomials with complex coefficients which improve upon some results due to Aziz and Mohammad, Govil and Rahman
Externí odkaz:
http://arxiv.org/abs/1511.02333
Autor:
Rather, N. A., Gulzar, Suhail
Let $D_\alpha P(z)=nP(z)+(\alpha-z)P^{\prime}(z)$ denote the polar derivative of a polynomial $P(z)$ of degree $n$ with respect to a point $\alpha\in\mathbb{C}.$ In this paper, we present a correct proof, independent of Laguerre's theorem, of an ineq
Externí odkaz:
http://arxiv.org/abs/1404.6600
Publikováno v:
Matemati\v{c}ki vesnik, 2014
Let $P(z)$ be a polynomial of degree $n$ having no zero in $|z|
Externí odkaz:
http://arxiv.org/abs/1403.2270
Autor:
Rather, N. A., Gulzar, Suhail
Publikováno v:
Appl. Math. E- Notes vol. 13 (2013), 155{159
In this paper, we obtain an annulus containing all the zeros of the polynomial involving binomial coefficients and generalized Fibonacci numbers. Our result generalize some of the recently obtained results in this direction.
Comment: 4 pages
Comment: 4 pages
Externí odkaz:
http://arxiv.org/abs/1312.0135
Autor:
Rather, N. A., Gulzar, Suhail
If $P(z)$ be a polynomial of degree at most $n$ which does not vanish in $|z| < 1$, it was recently formulated by Shah and Liman \cite[\textit{Integral estimates for the family of $B$-operators, Operators and Matrices,} \textbf{5}(2011), 79 - 87]{wl}
Externí odkaz:
http://arxiv.org/abs/1306.0714
In this paper, we present certain new $L_p$ inequalities for $\mathcal B_{n}$-operators which include some known polynomial inequalities as special cases.
Comment: 20 pages
Comment: 20 pages
Externí odkaz:
http://arxiv.org/abs/1304.0444