凸函数的Hadamard不等式的若干推广

本文获得两个定理 ,它们均是不等式f a +b2 1b -a∫baf (x) dx f (a) +f (b)2(其中 f是 [a,b]上的连续凸函数 )的推广 .     

Two Inequalities for Convex Functions

Let a ₀ < a ₁ < ··· < a _n be positive integers with sums $ {\sum\nolimits_{i = 0}^n {\varepsilon _{i} a_{i} {\left( {\varepsilon _{i} = 0,1} \right)}} } Let a ₀ < a ₁ < ··· < a _n be positive integers with sums distinct. P. Erd?s conjectured that The best known result along this line is that of Chen: Let f be any given convex decreasing function on [A, B] with α ₀, α ₁, ... , α _n , β ₀, β ₁, ... , β _n being real numbers in [A, B] with α ₀ ≤ α ₁ ≤ ··· ≤ α _n , Then In this paper, we obtain two generalizations of the above result; each is of special interest in itself. We prove: Theorem 1 Let f and g be two given non-negative convex decreasing functions on [A, B], and α ₀, α ₁, ... , α _n , β ₀, β ₁, ... , β _n , α' ₀, α' ₁, ... , α' _n , β' ₀ , β' ₁ , ... , β' _n be real numbers in [A, B] with α ₀ ≤ α ₁ ≤ ··· ≤ α _n , α' ₀ ≤ α' ₁ ≤ ··· ≤ α' _n , Then Theorem 2 Let f be any given convex decreasing function on [A, B] with k ₀, k ₁, ... , k _n being nonnegative real numbers and α ₀, α ₁, ... , α _n , β ₀, β ₁, ... , β _n being real numbers in [A, B] with α ₀ ≤ α ₁ ≤ ··· ≤ α _n , Then      

关于凸函数的新不等式

考虑由Fejér不等式的右边部分生成的差值.通过建立积分恒等式,在导函数满足M-Lipschitz条件和导函数有界这两种情况下,给出这个差值的界的估计.     

s-对数凸函数的Hermite-Hadamard型积分不等式

该文定义了"s-对数凸函数"的概念,并给出了可微s-对数凸函数的若干个HermiteHadamard型积分不等式,作为应用给出了平均数的几个不等式.     

Dominating Sets for Convex Functions with Some Applications

A number of optimization methods require as a first step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this paper, we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an infinite number of) convex functions, and we show how to obtain a convex dominating set in terms of dominating sets of simpler problems. The applicability of the results obtained is illustrated with the statement of new localization results in the fields of linear regression and location.     

Multiple Integral Inequalities for Schur Convex Functions on Symmetric and Convex Bodies

In this paper, by making use of Divergence theorem for multiple integrals, we establish some integral inequalities for Schur convex functions defined on bodies $B⊂\mathbb{R}^n$ that are symmetric, convex and have nonempty interiors. Examples for three dimensional balls are also provided.     

凸函数的几个Hadamard型不等式

对于凸函数建立了几个新的 Hadamard型不等式 ,比如f ∑nk=1qkak∫A+yA- yg(x) dx ∫A+yA- yf (x) g(x) dx ∑nk=1qkf (ak) ∫A+yA- yg(x) dx和f (pa +qb) p∫ξaf (x) g(x) dx∫ξag(x) dx+q∫bξf (x) g(x) dx∫bξg(x) dx pf (a) +qf (b)等 ,推广了前人所做的工作 .     

含有解析函数与亚纯函数的一些不等式

指出文献 [2 ]和文献 [4]中的错误 ,并且得到含有单位圆盘内接解析函数与亚纯函数的几个不等式 .     

凸体的宽度不等式及应用

该文建立了关于单形宽度的杨路、张景中不等式的一个逆不等式. 作为凸体宽度不等式的应用,得到了凸体的截面和投影的一些估计式.     

Several Hermite-Hadamard Typ e Inequalities for Harmonically Convex Functions in the Second Sense with Applications

In this paper, we first introduce the concept“harmonically convex func-tions”in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.     

Estimates for Integral Means of Hyperbolically Convex Functions

We prove the Mejia-Pommerenke conjecture that the Taylor coefficients of hyperbolically convex functions in the disk behave like O(log^?2(n)/n) as n → ∞ assuming that the image of the unit disk under such functions is a domain of bounded boundary rotation. Moreover, we obtain some asymptotically sharp estimates for the integral means of the derivatives of such functions and consider an example of a hyperbolically convex function that maps the unit disk onto a domain of infinite boundary rotation.     

若干函数不等式探析

针对近几年大学生高等数学竞赛和硕士研究生入学考试中出现的若干有关函数不等式的试题,探讨分析其命题背景,并推广深化相关结果.     

凸函数的双参数Jensen不等式链

使用组合理论,将凸函数的单参数Jensen不等式链推广为双参数的形式,从而获得一个新的Jensen不等式链.     

凸函数的双参数平均不等式的新证明

利用 Tchebycheff积分不等式和积分形式的 Cauchy中值定理证明了下列结论 :设 f(x)是 [a,b]上的正连续函数 ,且在 (a,b)内可微 ,若 f′(x)单调递增 ,则对任意的 p,q,有 Mp,q(f) 相似文献   

关于单形的几个不等式及其应用

Using theory of distance geometry and analytic method, the problem on relations about the volumes of some simplices is studied, and some new inequalities for the volumes of simplices are established. As special cases, an inequality for the volume of the pedal simplex of a simplex and other inequalities for simplices are gotten.