共查询到20条相似文献,搜索用时 31 毫秒
1.
Doklady Mathematics - In this paper, we consider sharp estimates of integral functionals $int_0^{2pi } {phi (L|Lf_n (t)|)dt} $ for functions φ defined on the semiaxis (0, ∞) and... 相似文献
2.
V. V. Arestov 《Mathematical Notes》1990,48(4):977-984
Translated from Matematicheskie Zametki, Vol. 48, No. 4, pp. 7–18, October, 1990. 相似文献
3.
Inequalities are conjectured for the Jacobi polynomials and their largest zeros. Special attention is given to the cases β = α − 1 and β = α.
相似文献
4.
A. V. Olesov 《Siberian Mathematical Journal》2010,51(4):706-711
We sharpen and supplement the results by V. I. Smirnov, A. Aziz, and Q. M. Dawood for algebraic polynomials which generalize the classical Bernstein and Erdos-Lax inequalities. 相似文献
5.
6.
LetP(z) be a polynomial of degreen which does not vanish in the disk |z|<k. It has been proved that for eachp>0 andk≥1, $$\begin{gathered} \left\{ {\frac{1}{{2\pi }}\int_0^{2\pi } {\left| {P^{(s)} (e^{i\theta } )} \right|^p d\theta } } \right\}^{1/p} \leqslant n(n - 1) \cdots (n - s + 1) B_p \hfill \\ \times \left\{ {\frac{1}{{2\pi }}\int_0^{2\pi } {\left| {P(e^{i\theta } )} \right|^p d\theta } } \right\}^{1/p} , \hfill \\ \end{gathered} $$ where $B_p = \left\{ {\frac{1}{{2\pi }}\int_0^{2\pi } {\left| {k^s + e^{i\alpha } } \right|^p d\alpha } } \right\}^{ - 1/p} $ andP (s)(z) is thesth derivative ofP(z). This result generalizes well-known inequality due to De Bruijn. Asp→∞, it gives an inequality due to Govil and Rahman which as a special case gives a result conjectured by Erdös and first proved by Lax. 相似文献
7.
We prove that an absolute constantc>0 exists such that
相似文献
8.
Horst Alzer 《Proceedings Mathematical Sciences》2010,120(2):131-137
Let n ≥ 1 be an integer and let P
n
be the class of polynomials P of degree at most n satisfying z
n
P(1/z) = P(z) for all z ∈ C. Moreover, let r be an integer with 1 ≤ r ≤ n. Then we have for all P ∈ P
n
:
|