共查询到20条相似文献,搜索用时 78 毫秒
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讨论了指数多项式不等式的自动证明问题,运用Taylor展开式将目标不等式的证明转化为一系列的一元多项式不等式的验证,然后借助代数不等式证明工具(如Bottema)完成最后的工作.运用Maple实现了上述算法,算法对所有指数多项式不等式终止,并且可以输出"可读"的证明过程. 相似文献
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受凸体的Steiner多项式的启发,定义了星体的对偶Steiner多项式,并利用对偶Aleksandrov-Fenchel不等式讨论了对偶Steiner多项式的根.进而,得到了关于对偶Steiner多项式的根的一些不等式,这些不等式恰好是关于Steiner多项式的根的不等式的对偶形式. 相似文献
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本文首先对双周期缺项插值多项式得到了一个不等式,它是Birkhoff插值的不等式的推广.然后,应用这个不等式研究双周期缺项插值多项式平均逼近A(|z|≤1)中的函数得到了阶的估计.最后,还得到了一般的双周期缺项插值多项式收敛性的结果. 相似文献
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得到了一类变形的传输不等式,给出了判断其是否成立的充分条件和必要条件,并且利用这类不等式,对于指数阶矩不存在的概率测度,建立了相应的多项式型的聚集不等式. 相似文献
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讨论了形如f(x,trans1(x),…,transn(x))>0的超越函数多项式不等式的自动证明问题,运用Taylor展开式将目标不等式的证明转化为一系列的一元多项式不等式的验证,然后借助代数不等式证明工具完成最后的工作.运用Maple实现了上述算法,算法对常见超越函数多项式不等式十分高效,并且可以输出"可读"的证明过程. 相似文献
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应用实系数多项式的性质构造了一类满足Turan型不等式的多项式序列,证明了该多项式序列的几个性质,并给出了一些应用. 相似文献
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徐俊峰 《纯粹数学与应用数学》2015,(5):441-448
利用精简计数函数证明了关于φf2f(k)-1的定量估计不等式,这里f是一个超越亚纯函数,φ是关于f的小函数.此不等式推广了以往的结果. 相似文献
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沈云海 《数学的实践与认识》2006,(9)
首先研究了L2ω(-1,1)上关于L egendre多项式Xn(x)的L andau′s型不等式.利用Xn(x)的正交性,建立了代数多项式pn(x)的L andau′s型不等式,并且指出其不等式的系数在某种意义上是最好可能的. 相似文献
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Igor E. Pritsker 《Journal of Approximation Theory》2002,118(2):163-174
We study asymptotic behavior of the derivatives of Faber polynomials on a set with corners at the boundary. Our results have applications to the questions of sharpness of Markov inequalities for such sets. In particular, the found asymptotics are related to a general Markov-type inequality of Pommerenke and the associated conjecture of Erd
s. We also prove a new bound for Faber polynomials on piecewise smooth domains. 相似文献
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研究了代数多项式导数的Bernstein不等式和Markov不等式.通过代数多项式导数的一个积分表示式,给出这两个著名不等式以及它们的离散形式的证明. 相似文献
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用Schur分拆证明一类含参数的不等式 总被引:2,自引:0,他引:2
利用对称多项式的Schur分拆方法,以及单变元多项式实根隔离算法,证明了一个不等式猜想.并将这一方法用于处理一类含有参数的有理对称不等式. 相似文献
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Wathiq Bani-Domi 《Linear and Multilinear Algebra》2013,61(4):421-427
We prove a numerical radius inequality for operator matrices, which improves an earlier inequality due to Hou and Du. As an application of this numerical radius inequality, we derive a new bound for the zeros of polynomials. 相似文献
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利用Orlicz空间内有关不等式技巧在Orlicz空间内研究了用三角多项式的倒数逼近周期可微函数的问题.得到了一个逼近定理及其推论. 相似文献
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Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szegő's bounds on the zeros of Jacobi polynomials for , are completed with results for the rest of parameter values, Grosjean's inequality (J. Approx. Theory 50 (1987) 84) on the zeros of Legendre polynomials is shown to be valid for Jacobi polynomials with |β|1, bounds on ratios of consecutive zeros of Gauss and confluent hypergeometric functions are derived as well as an inequality involving the geometric mean of zeros of Bessel functions. 相似文献
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Lawrence A. Harris 《Journal of Mathematical Analysis and Applications》2008,338(1):350-357
This article considers the extension of V.A. Markov's theorem for polynomial derivatives to polynomials with unit bound on the closed unit ball of any real normed linear space. We show that this extension is equivalent to an inequality for certain directional derivatives of polynomials in two variables that have unit bound on the Chebyshev nodes. We obtain a sharpening of the Markov inequality for polynomials whose values at specific points have absolute value less than one. We also obtain an interpolation formula for polynomials in two variables where the interpolation points are Chebyshev nodes. 相似文献
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In this paper, we obtain an extension of the Pólya inequality for univariate real polynomials in L p spaces and new estimates for certain class of measurable sets. Inequalities for complex polynomials are also considered. We give an application to a multipoint best local approximation problem for real and complex polynomials. 相似文献