Inequalities

<正>When am I ever going to use this?BREAKFAST The table shows the nutrition requirements for a healthy breakfast cereal with milk.1.Suppose your favorite cereal has 2 grams of fat,7 grams of protein,4 grams of fiber,and 3 grams of sugar.Is it a healthy cereal? Explain.     

Lq Inequalities and Operator Preserving Inequalities

Let Pn be the class of polynomials of degree at most nRather and Shah [15]proved that if P∈Pnand P(z)≠0 in|z| 1, then for every R 0 and 0≤q ∞,|B[ P( Rz)]|q ≤|RnB[zn] + λ0 |q|1 + zn|q|P(z)|q,where B is a Bn-operator.In this paper, we prove some generalization of this result which in particular yields some known polynomial inequalities as specialWe also consider an operator Dαwhich maps a polynomial P(z) into DαP(z) := n P(z) +(α-z) P′(z) and obtain extensions and generalizations of a number of well-known Lq inequalities     

Gwinner变分不等式和隐变分不等式

本文在研究Gwinner变分不等式的基础上，利用新的集值映象不动点定理，探讨一类具广泛意义的隐变分不等式问题，改进了迄今相关结果中对紧性条件的要求，在非紧设置下获得了解的存在性定理．     

关于广义变分不等式与广义拟变分不等式

本文在非常一般的框架下,建立了极大极小不等式,广义变分不等式和广义拟变分不等式,证明了解的存在定理,且它们是在非紧集上得到的,从而推广和改进了[3～13]中的相应结果.     

关于广义双拟变分不等式和拟变分不等式

研究了一类广义双拟变分不等式和广义拟变分不等式解的存在性，推广、改进、统一了一些近期的相关结果．     

Concentration Inequalities for Bounded Functionals via Log-Sobolev-Type Inequalities

Journal of Theoretical Probability - In this paper, we prove multilevel concentration inequalities for bounded functionals $$f = f(X_1, \ldots , X_n)$$ of random variables $$X_1, \ldots , X_n$$...     

Correlation Inequalities

The main point of this note is to give a simple semigroup proof of a correlation inequality due to Hu , [H]. We also recover recent correlation inequalities due to Houdré , Pérez–Abreu and Surgailis , [HPS] and obtain some new correlation inequalities on Lie groups.     

关于三个未解决的不等式问题

通过求二阶导数或列举反例的方法可解决《常用不等式（第四版）》末尾提出的问题3、问题13和问题62,另外,利用Lyapunov不等式及Moran不等式可给出其问题190中一个不等式的下界.     

中点不等式和梯形不等式的量子模拟

建立了涉及二阶q-导数的积分恒等式,使用这个恒等式获得二阶可微函数中点不等式和梯形不等式的量子模拟.     

向量变分不等式与广义变分不等式之间的某些关系

文章首先建立了向量变分不等式与广义变分不等式之间的等价关系,然后利用这个结论,建立了向量变分不等式的Levitin-Polyak适定性与广义变分不等式的Levitin-Polyak适定性之间的等价关系.     

非紧集上的变分不等式与拟变分不等式

本文在非常一般的框架和较弱的条件下证明了一类变分不等式与拟变分不等式解的存在性，将［１－７］的结果作了推广并改进在非紧集上讨论     

Semi-Discrete Ingham-Type Inequalities

One of the general methods in linear control theory is based on harmonic and non-harmonic Fourier series. The key of this approach is the establishment of various suitable adaptations and generalizations of the classical Parseval equality. A new and systematic approach was begun in our papers [1]-[4] in collaboration with Baiocchi. Many recent results of this kind, obtained through various Ingham-type theorems, were exposed recently in [9]. Although this work concentrated on continuous models, in connection with numerical simulations a natural question is whether these results also admit useful discrete versions. The purpose of this paper is to establish discrete versions of various Ingham-type theorems by using our approach. They imply the earlier continuous results by a simple limit process.     

加权拟变分不等式

本文介绍了Stampacchia型和Minty型加权拟变分不等式以及加权拟变分不等式组,并讨论了它们之间的关系.利用这种关系研究了加权拟变分不等式和加权拟变分不等式组的解的存在性.     

Polynomial Lym Inequalities

For a Sperner family A 2^[n] let A _i denote the family of all i-element sets in A. We sharpen the LYM inequality by adding to the LHS all possible products of fractions , with suitable coefficients. A corresponding inequality is established also for the linear lattice and the lattice of subsets of a multiset (with all elements having the same multiplicity).* Research supported by the Sonderforschungsbereich 343 Diskrete Strukturen in der Mathematik, University of Bielefeld.