相关论文: A mean value theorem for systems of integrals

In this paper, we prove Smale's mean value conjecture by making use of quasiconformal deformations and holomorphic motions.

Suppose that $\Gamma_0\subset\mathbb R^{n+1}$ is a closed countably $n$-rectifiable set whose complement $\mathbb R^{n+1}\setminus \Gamma_0$ consists of more than one connected component. Assume that the $n$-dimensional Hausdorff measure of…

Let (M,g) be a non-compact and complete Riemannian manifold with minimal horospheres and infinite injectivity radius. We prove that bounded functions on (M,g) satisfying the mean-value property are constant. We extend thus a result of A.…

The random convex hull of a Poisson point process in $\mathbb{R}^d$ whose intensity measure is a multiple of the standard Gaussian measure on $\mathbb{R}^d$ is investigated. The purpose of this paper is to invent a new viewpoint on these…

We establish an integral representation for Popoviciu's convex functions of $d$ variables. This representation serves as a~foundation for deriving several functional inequalities, analogous to those well-known for usual convex functions.…

We establish a Fenchel-Moreau type theorem for proper convex functions $f\colon X\to \bar{L}^0$, where $(X, Y, \langle \cdot,\cdot \rangle)$ is a dual pair of Banach spaces and $\bar L^0$ is the space of all extended real-valued functions…

A classical problem in number theory is showing that the mean value of an arithmetic function is asymptotic to its mean value over a short interval or over an arithmetic progression, with the interval as short as possible or the modulus as…

In this paper, we study the existence of fixed points for mappings defined on complete metric space (X, d) satisfying a general contractive inequality of integral type depended on another function. This conditions is analogous of Banach…

The general dual volume $\dveV(K)$ and the general dual Orlicz curvature measure $\deV(K, \cdot)$ were recently introduced for functions $G: (0, \infty)\times \sphere\rightarrow (0, \infty)$ and convex bodies $K$ in $\R^n$ containing the…

The discrete data encoded in the power moments of a positive measure, fast decaying at infinity on euclidean space, is incomplete for recovery, leading to the concept of moment indeterminateness. On the other hand, classical integral…

We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…

A celebrated result of Hal\'asz describes the asymptotic behavior of the arithmetic mean of an arbitrary multiplicative function with values on the unit disc. We extend this result to multilinear averages of multiplicative functions…

In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in R^n belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors…

In this short note we prove that, if (C[a,b],{A_n}) is an approximation scheme and (A_n) satisfies de La Vall\'ee-Poussin Theorem, there are instances of continuous functions on [a,b], real analytic on (a,b], which are poorly approximable…

We show that for any bounded function $f:[a,b]\rightarrow{\mathbb R}$ and $\epsilon>0$ there is a partition $P$ of $[a,b]$ with respect to which the Riemann sum of $f$ using right endpoints is within $\epsilon$ of the upper Darboux sum of…

The notion of a valuation on convex bodies is very classical. The notion of a valuation on a class of functions was recently introduced and studied by M. Ludwig and others. We study an explicit relation between continuous valuations on…

We investigate the properties of convex functions in the plane that satisfy a local inequality which generalizes the notion of sub-solution of Monge-Ampere equation for a Monge-Kantorovich problem with quadratic cost between non-absolutely…

Suppose $D$ is a suitably admissible compact subset of $\mathbb{R}^k$ having a smooth boundary with possible zones of zero curvature. Let \mbox{$R(T,\theta,x)= N(T,\theta,x) - T^{k}\mathrm{vol}(D)$,} where $N(T,\theta,x)$ is the number of…

In this paper, we investigate Liu-Xu-Ye-Zhao's conjecture [30] and prove a sharp convergence theorem for the mean curvature flow of arbitrary codimension in spheres which improves the convergence theorem of Baker [2] as well as the…

Regular variation of a multivariate measure with a Lebesgue density implies the regular variation of its density provided the density satisfies some regularity conditions. Unlike the univariate case, the converse also requires regularity…