共查询到20条相似文献,搜索用时 64 毫秒
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经典的仿射均质积分不等式是Brunn-Minkowski理论中一个关键不等式.建立了Lp Brunn-Minkowski型仿射均质积分不等式,定义了Lp Brunn-Minkowski型仿射混合均质积分且推广得到了Lp Brunn-Minkowski型仿射混合均质积分不等式. 相似文献
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《数学物理学报(A辑)》2018,(6)
该文获得了R~n中星体弦长积分的一些极限性质,建立了星体弦长积分的不等式,包括弦长积分和对偶均质积分之间的不等式以及对偶Blaschke-Santaló不等式. 相似文献
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通过适当构造辅助函数和应用牛顿—莱布尼兹公式、施瓦兹积分不等式,将一个特定型定积分不等式进行了推广.证明了只要被积函数在积分区间内存在零点,该特定型定积分不等式均成立,进而给出实例说明了该不等式成立的正确性. 相似文献
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建立了一类二变量的积分不等式,该不等式包含了一个一重积分和两个二重积分.利用分析技巧,给出了积分不等式中未知函数的估计.这一结果可以作为研究积分-微分方程解的定性性质的工具. 相似文献
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首先利用Hlder不等式证明一个弦幂积分不等式,然后利用该不等式获得了一个类似于Maclaurin的弦幂积分不等式. 相似文献
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一类积分不等式的推广 总被引:1,自引:0,他引:1
对一些基本的积分不等式进行了推广,给出了含有n个无关变元的更广泛的非线性积分不等式.利用所得的不等式讨论了某些非线性积分方程解的有界性. 相似文献
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通过几道常见的定积分不等式证明例题,从不同角度分析、研究定积分不等式的特点,归纳总结出构造辅助函数,利用重要积分公式、性质、定积分中值定理及重要不等式等证明定积分不等式的七种典型方法. 相似文献
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一个推广的二变量时滞积分不等式及其应用 总被引:1,自引:1,他引:0
建立了一类二变量的时滞积分不等式,不等式包含一个一重积分和两个二重积分,二重积分内包含两个不同的没有假设单调性的未知函数的复合函数.使用单调化技术,给出积分不等式中未知函数的估计.结果能对相关文献中考虑的积分不等式中未知函数进行估计.进一步,结果给出了一类积分-微分方程解的估计. 相似文献
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In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature. 相似文献
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In this paper, sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg
group are given. The necessity is discussed by polar coordinates changes of the Heisenberg group. Establishing a class of
Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation,
we derive the sufficiency. Finally, sharp constants for Hardy type inequalities are determined. 相似文献
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Fethi SOLTANI 《数学研究及应用》2022,42(1):8-14
In this work,we prove Clarkson-type and Nash-type inequalities for the Laguerre transform■on M=[0,∞)×R.By combining these inequalities,we show Laeng-Morpurgo-type uncertainty inequalities.We establish also a local-type uncertainty inequalities for the Laguerre transform■,and we deduce a Heisenberg-Pauli-Weyl-type inequality for this transform. 相似文献
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利用积分几何中估计包含测度的思想给出常曲率平面上一些新的逆Bonnesen型不等式.这些不等式在欧氏平面上为著名的Bottema不等式的改进形式与新的逆Bonnesen型不等式. 相似文献
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Gord Sinnamon 《Proceedings of the American Mathematical Society》2004,132(2):375-379
Weighted Opial-type inequalities are shown to be equivalent to weighted norm inequalities for sublinear operators and for nearly positive operators. Examples involving the Hardy-Littlewood maximal function and the nonincreasing rearrangement are presented.
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In this paper, we consider Carlson type inequalities and discuss their possible improvement. First, we obtain two different types of generalizations of discrete Carlson's inequality by using the Hlder inequality and the method of real analysis, then we combine the obtained results with a summation formula of infinite series and some Mathieu type inequalities to establish some improvements of discrete Carlson's inequality and some Carlson type inequalities which are equivalent to the Mathieu type inequalities. Finally, we prove an integral inequality that enables us to deduce an improvement of the Nagy-Hardy-Carlson inequality. 相似文献
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基于研究对数Sobolev,Nash和其它泛函不等式的需要,将Poincare不等式 的变分公式拓广到一大类直线上函数的Banach(Orlicz)空间.给出了这些不等式成立 与否的显式判准和显式估计. 作为典型应用,仔细考察了对数Sobolev常数. 相似文献
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George A. Anastassiou 《Applicable analysis》2013,92(5):607-624
Here we present univariate Sobolev-type fractional inequalities involving fractional derivatives of Canavati, Riemann–Liouville and Caputo types. The results are general L p inequalities forward and converse on a closed interval. We give an application to a fractional ODE. We present also the mean Sobolev-type fractional inequalities. 相似文献