Second Order Differential-functional Inequalities for Bounded Functions

We prove a differential-functional version of the Lemma of Nagumo and Westphal which can be applied to differential-functional inequalities for bounded C -functions on having bounded derivatives. As an application an existence and uniqueness result for bounded solutions of linear second order differential-functional equations is proved.     

Exact Kolmogorov-Type Inequalities with Bounded Leading Derivative in the Case of Low Smoothness

We obtain new unimprovable Kolmogorov-type inequalities for differentiable periodic functions. In particular, we prove that, for r = 2, k = 1 or r = 3, k = 1, 2 and arbitrary q, p [1, ], the following unimprovable inequality holds for functions :

加权(C)eby(s)ev-Ostrowski型不等式

关于著名的Cebysev不等式，已有众多的研究成果．通过建立积分不等式，来建立全新的加权Cebysev型积分不等式．给予了独立的证明，并给出了此类不等式的新评价．     

Improved Bonferroni Inequalities and Binomially Bounded Functions

We introduce the concept of a binomially bounded function and associate with each such function an improved Bonferroni-type inequality.     

On Kolmogorov-Type Inequalities Taking into Account the Number of Changes in the Sign of Derivatives

For 2-periodic functions and arbitrary q [1, ] and p (0, ], we obtain the new exact Kolmogorov-type inequality which takes into account the number of changes in the sign of the derivatives (x ^(k)) over the period. Here, = (r – k + 1/q)/(r + 1/p), _r is the Euler perfect spline of degree r, and . The inequality indicated turns into the equality for functions of the form x(t) = a _r (nt + b), a, b R, n N. We also obtain an analog of this inequality in the case where k = 0 and q = and prove new exact Bernstein-type inequalities for trigonometric polynomials and splines.     

Omniscience Principles and Functions of Bounded Variation

A very weak omniscience principle is formulated, related omniscience principlesare considered, and the theorem that a function of bounded variation is the difference of two increasing functions is shown to be equivalent to the omniscience principle WLPO. It is a so shown that an arbitrary function (not necessarily strongly extensional) with located variation on an interval is the difference of two increasing functions.     

Floating Drops and Functions of Bounded Variation

A variational problem for three fluids in which gravitational and surface tension forces are in equilibrium is studied using sets of finite perimeter and functions of bounded variation. Existence theorems are proven which imply the existence of an axisymmetric floating drop. This problem has been studied previously as a free boundary problem for axisymmetric capillary surfaces by Elcrat, Neel and Siegel, but the general existence problem for arbitrary drop volumes was left open. The results presented here settle a version of this question.     

关于一般矩阵函数变差的不等式

该文首先展示了一般矩阵函数dχ(A)=∑[DD(X]σ∈H[DD)]χ(σ)∏[DD(]m[]i=1[DD)]aiσ(i)可作为一个酉空间张量的适当对称类的内积.然后，借助Schwarz不等式和范数证明了关于一般矩阵函数变差的三个主要不等式,而其中一个不等式是已知不等式的推广.     

Inequalities for the Derivatives of Rational Functions with Real Zeros

We study Turán-type inequalities for the derivatives of rational functions, whose zeros are all real and lie inside [-1,1] but whose poles are outside (-1,1), in the supremum- and L2-norms respectively. We generalize several well-known results for classical polynomials. We also obtain a sharp L2 Bernstein-type inequality for the rational system with prescribed poles.     

导数具有k阶分担小函数的亚纯函数

主要讨论亚纯函数的导数具有某些k阶分担小函数时的唯一性问题,得到一个有趣的结果,推广了作者近期的一个结果..     

Unconditional Convergence of Fourier Series for Functions of Bounded Variation

This article concerns the unconditional convergence a.e. of Fourier series with respect to general orthonormal systems. We find certain conditions to be satisfied by the functions in the orthonormal system so that the Fourier series of each function of finite variation unconditionally converge a.e. The results are best possible.     

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 $$X_1, \ldots , X_n$$...     

A Constructive Look at Functions of Bounded Variation

Functions with bounded variation and with a (total) variationare examined within Bishop's constructive mathematics. It isshown that the property of having a variation is hereditarydownward on compact intervals, and hence that a real-valuedfunction f with a variation on a compact interval can be expressedas a difference of two increasing functions. Moreover, if fis sequentially continuous, then the corresponding variationfunction, and hence f itself, is uniformly continuous. 1991Mathematics Subject Classification 26A45.     

On Bounded Variation Functions by General MKZD Operators

In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.     

Real-Linear Isometries on Spaces of Functions of Bounded Variation

Let X and Y be subsets of the real line with at least two points. We study the surjective real-linear isometries \({T:BV(X)\longrightarrow BV(Y)}\) between the spaces of functions of bounded variation on X and Y with respect to the supremum norm \({\|\cdot\|_\infty}\) and the complete norm \({\|\cdot\|:=\max(\|\cdot\|_\infty,\mathcal{V}(\cdot))}\), where \({\mathcal{V}(\cdot)}\) denotes the total variation of a function. Additively norm preserving maps between these spaces are also characterized as a corollary.     

模糊有界变差函数全变差的积分表示与距离导数

定义和讨论了模糊数值函数的距离导数,给出了模糊有界变差函数全变差的积分表示.发现模糊绝对连续函数是几乎处处距离可导的,距离导数的积分等于其原函数的总变差,从而给出了模糊有界变差函数全变差的积分表示.