广义Heronian平均与幂平均的最优比较

比较了含有两个参数的广义Heronian平均H_(p,W)(a,b)与幂平均M_q(a,b)的大小,得到了M_q(a,b)≥(≤)H_(p,w)(a,b)对于任意a,b>0成立的充要条件.     

Set-Valued Means

Set-Valued and Variational Analysis - The notion of set-valued means is introduced. Set-valued counterparts of the arithmetic, quasi-arithmetic and Lagrangian means are investigated and various...     

Weighted Harmonic Means

The purpose of this study is to develop a conception of the differential subordination involving harmonic means of the expressions \(\psi (p(z), zp'(z);z)\), where p is an analytic function in the unit disk, such that \(p(0)=1, p(z)\not \equiv 1\). Here, we discuss convex weighted harmonic means and we find some applications in the theory of analytic functions.     

Means on solenoids

It is determined which solenoids admit 2-argument continuous means.

     

Means of iterates

Aequationes mathematicae - We determine continuous bijections f, acting on a real interval into itself, whose k-fold iterate is the quasi-arithmetic mean of all its subsequent iterates from $$f^0$$...     

Means on equivalence relations

Suppose that X is a Polish space and E is a countable Borel equivalence relation on X. We show that if there is a Borel assignment of means to the equivalence classes of E, then E is smooth. We also show that if there is a Baire measurable assignment of means to the equivalence classes of E, then E is generically smooth. Research partially supported by NSF Grants DMS-9987437 and DMS-0455285. Research partially supported by NSF VIGRE Grant DMS-0502315.     

Equivalence of Integral Means

Let Aρf and Lρf be the integral means of f on a ball Bρ and its sphere, respectively. Frequently they are regarded as a bridge because of the smoothness. In this paper we will investigate their equivalence. More precisely, we will prove, among others, the following relationship: for any 1 ≤ p ≤ ∞ and d ≥ 2, $$\parallel A_\rho f-f\parallel _p\sim \parallel L_\rho f-f\parallel _p,\quad \forall f\in L^p({\rm R}^d).$$      

4-points Stolasky Means

In this paper we define Stolarsky type means for 4 points. Some special cases of our means represents an explicit form of means defined through divided means in [3]. As in classical case, we also show monotonicity property of new means.     

一些平均值的比较

利用关于广义平均值进行比较的已知结果去比较幂平均值、Stolarsky平均值和Heron平均值,简化了某些结果的证明,并得到了一些新的结果.     

Means and their applications

General considerations about means and expectations are preceded by a short historical overview. The existing approaches to the definition of means are classified into three groups: approximational, functional, and axiomatic. In some particular cases all of them are equivalent. The problem of meaningfulness of means is discussed for ordinal data and for some important cases of metric data. A survey of the main areas of applications: decision theory, group decision, insurance, economical equity and inequality is also provided. This revised version was published online in June 2006 with corrections to the Cover Date.     

Means on chainable continua

By a mean on a space we understand a mapping such that and for . A chainable continuum is a metric compact connected space which admits an - mapping onto the interval for every number . We show that every chainable continuum that admits a mean is homeomorphic to the interval. In this way we answer a question by P. Bacon. We answer some other questions concerning means as well.

     

On Riesz Means of Eigenvalues

In this article we prove the equivalence of certain inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian with a classical inequality of Kac. Connections are made via integral transforms including those of Laplace, Legendre, Weyl, and Mellin, and the Riemann–Liouville fractional transform. We also prove new universal eigenvalue inequalities and monotonicity principles for Dirichlet Laplacians as well as certain Schrödinger operators. At the heart of these inequalities are calculations of commutators of operators, sum rules, and monotonic properties of Riesz means. In the course of developing these inequalities we prove new bounds for the partition function and the spectral zeta function (cf. Corollaries 3.5–3.7) and conjecture about additional bounds.     

Fourier-Jacobi展开的Riesz平均

对ｆ∈Ｌｐ（Ｒ＋，Δ（ｔ）ｄｔ），Δ（ｔ）＝（２ｓｉｎｈｔ）２α＋１（２ｃｏｓｈｔ）２β＋１，１ｐ２，本文证明了当Ｒｅｚ＞（２／ｐ－１）（α＋１／２）时，ｆ的Ｆｏｕｒｉｅｒ－Ｊａｃｏｂｉ展开的ｚ－阶Ｒｉｅｓｚ平均几乎处处收敛于ｆ．该结果推广了Ｇｉｕｌｉｎｉ和Ｍａｕｃｅｒｉ在实秩为１的对称空间上的相应结果     

Uniform Mixtures Via Posterior Means

The problem of identification of uniform mixtures via posterior means is studied. For linear posterior means a complete solution is given. It determines a family of prior distributions involving beta of both kinds and gamma. Identifiability via any consistent posterior mean is also investigated.     

On Fejer and Bochner-Riesz Means

For the Fejer means on an equivalence between the rate of its convergence and an appropriate K-functional is established. For the Bochner-Riesz means on an equivalence between the rate of convergence and the corresponding K-functional is obtained. The results are of the form of strong converse inequality of type A.     

Monotonicity of Average Power Means

A new numerical inequality for average power means is presented. Let and let be a sequence of positive numbers. Consider the operator . We denote by the superposition of these operators. The following assertion is proved: if . Bibliography: 2 titles.     

On Means of Nonnegative Sesquilinear Forms

The aim of this paper is to generalize the theory of operator connections for nonnegative sesquilinear forms. As an application, we investigate the case of bounded finitely additive set functions. One of the most important connections in this setting is the parallel sum. We introduce this notion, and in addition, we present a Lebesgue-type decomposition theorem for such functions.