一类对称函数不等式的加细和推广

利用控制不等式理论加细和推广了一类对称函数不等式,并给出一个几何应用。     

一个加细的反向Jensen不等式

文 [1 ]在函数的凸性理论中 ,给出了一个重要的结论 :设 f ( x)、p( x)为 I上的可积函数 ,而 m≤ f ( x)≤ M,p( x)≥ 0 ,∫Ip( x) dx >0 ,则随连续函数Φ( t) ( m≤ t≤ M)之为下凸或上凸而相应地有Φ∫Ip( x) f ( x) dx∫Ip( x) dx≤或≥∫Ip( x) f ( x) dx∫Ip( x) dx(即 Jensen不等式 )　　为证明其反向不等式 ,引入以下记号 ,并引入严格凸函数的一个几何性质。记 I =[a,b];∫I=∫ba;A( f ( x) ) =∫Ip( x) f ( x) dx∫Ip( x) dx为 f ( x)的加权平均 ,p( x)≥ 0 ,∫Ip( x) dx >0 ,x∈ I。设Φ( x) >0 ,Φ″( x) >0 ,x∈ I,则Φ( …     

关于广义对数平均的一个不等式的加细

In this article,we show that the generalized logarithmic mean is strictly Schurconvex function for p＞2 and strictly Schur-concave function for P＜2 on R2+.And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.     

一个全平面上含混合核的Hilbert型不等式

引入多个参数,利用正割函数的有理分式展开形式,建立了一个最佳常数因子与正割函数的偶数阶导数有关的,并定义在R×R上的Hilbert型积分不等式及其等价形式.特别地,赋予参数不同的数值,文末还建立了一些特殊的Hilbert型不等式.     

两个三角形不等式的串联与加细

对文[1]中给出的两个三角形不等式进行研究,通过加细,得到了串联起这两个不等式的一个不等式“链”.     

调和凸函数及其Hermite-Hadamard型不等式的加细

完善调和凸函数的基本性质,并利用两个函数对调和凸函数的Hermite-Hadamard型不等式进行加细.     

关于凸函数的一个控制不等式

关于凸函数的一个控制不等式续铁权（青岛教育学院数学系２６６０７１）设ｆ（ｘ）在［ａ，ｂ］上定义，０＜ｔ＜１，若称ｆ（ｘ）是［ａ，ｂ］上的凸函数，若当时严格不等式成立，称ｆ（ｘ）是严格凸函数．若不等式反向，称ｆ（ｘ）是凹函数和严格凹函数．本文研究凸函数...     

关于度量加的一个定理及一个矩阵不等式

关于度量加的一个定理及一个矩阵不等式苏化明（合肥工业大学数学力学系２３０００９）§１关于度量加的一个定理Ｒ。Ａｌｅｘａｎｄｅｒ在［１］中曾提出如下猜想：设两个单形的顶点分别为ｐ＿１，Ｐ＿２，…，Ｐ＿（ｎ＋１），和构作第三个单形，使得测应当有不等式这里...     

Stability of the linear inequality method for rational Chebyshev approximation

The linear inequality method is an algorithm for discrete Chebyshev approximation by generalized rationals. Stability of the method with respect to uniform convergence is studied. Analytically, the method appears superior to all others in reliability.     

Adamovic''''s不等式的推广与加细

In this article, by means of the theory of majorization, Adamovic's inequality is extended to the cases of the general elementary symmetric functions and its duals, and the refined and reversed forms are also given. As applications, some new inequalities for simplex are established.     

Improvement of Newman inequality

Let . Newman inequality is

     

Muirhead-Rado inequality for compact groups

Muirhead’s majorization inequality was extended by Rado to the case of arbitrary permutation groups. We further generalize this inequality to compact groups and their linear representations over the reals. We characterize saturation of the inequality, and describe the saturation condition in detail for the case of actions on Hermitian operators. Supported in part by the National Science Foundation and the Center for the Mathematics of Information.     

A Turán type inequality for rational functions with prescribed poles

Summary By employing a novel idea and simple techniques, we substantially generalize the Turán type inequality for rational functions with real zeros and prescribed poles established by Min [5] to include L^pspaces for 1≤p≤∞<span style='font-size:10.0pt'>while loosing the restriction ρ > 2 at the same time.     

A Turán type inequality for rational functions with prescribed poles

Summary By employing a novel idea and simple techniques, we substantially generalize the Turán type inequality for rational functions with real zeros and prescribed poles established by Min [5] to include L^p spaces for 1≤ p ≤ ∞ while loosing the restriction ρ > 2 at the same time.     

Refinements of the Heinz operator inequalities

In this article, we study the Heinz inequalities for two positive operators. We refine the ordering relations among the Heinz means with different parameters and obtain some improvements of the Heinz operator inequalities.     

Refinements of generalized triangle inequalities

In this paper, we discuss refinements of the well-known triangle inequality and it is reverse inequality for strongly integrable functions with values in a Banach space X. We also discuss refinement of a generalized triangle inequality of the second kind for Lp functions. For both cases, the attainability of the equality is also investigated.     

A bernstein type inequality for derivatives of rational functions on two intervals

In this paper we establish an inequality for derivatives of rational functions with a fixed denominator generalizing V. S. Videnskii's inequality to the case of two intervals. To prove its asymptotic exactness, we use a new representation of Akhiezer-Zolotarev fractions with the least deviation from 0 on two intervals. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 508–514, October, 1999.