数学专业毕业论文（设计）-浅谈凸函数及其应用.docVIP

目录 摘要…………………………………………………………………………… 1 引言…………………………………………………………………………… 2 一 凸函数概念及其定义………………………………………………………3 （一）凸函数的几种不同定义 ………………………………………………3 （二）几种不同定义之间的相互联系 ………………………………………5 二 凸函数的有关结论…………………………………………………………6 （一）凸函数的运算性质 ……………………………………………………6 （二）凸函数的其它性质 ……………………………………………………7 （三）凸函数的充要条件 ……………………………………………………9 三 对数性凸函数的定义及其性质……………………………………………11 （一）对数性凸函数的定义 …………………………………………………12 （二）对数性凸函数的基本性质 ……………………………………………13 （三）与对数性凸函数的性质相关的定理 …………………………………14 （四）对数性凸函数性质的应用 ……………………………………………15 结束语 …………………………………………………………………………17 参考文献 ………………………………………………………………………17 浅谈凸函数及其应用 王建 （渤海大学 数学系 辽宁锦州121000）Jensen）H?lder）不等式、闵可夫斯基（Minkowski）不等式及一些初等不等式. 关键词：凸函数; 对数性凸函数；不等式;证明;应用 Convex Function and its Application Wang Jian (Department of Mathematics Bohai University Liaoning Jinzhou 121000 China) Abstract: convex function is a kind of important function ,its concept form most early in Jensen in the writing .It has numerous application in broad fields of pure Mathematics and applied Mathematics .Convex function is now plays important theoretical basic and useful tools to mang subjects such as mathematical planning theory ,response theory ,numerical economics ,change ho theory and sub-optimal control and so on .For theoretical breakthrough,reinforce their application in practice, produced generalized convex function. Enumerated convex function is introduced several famous inequality logarithmic ratio convex function concept, won the logarithmic ratio some basic properties of convex function, and discussed the logarithmic ratio of basic properties of convex function by some of the application, the inspiration of [1], [1] in the basis, in this paper, we obtain the logarithmic sex convex function is seven basic properties, and discusses the properties of logarithmic ratio convex function applications. This paper investigates the criterions of convex function and its applications based on the definition of convex function, summarizes many important properties of convex functions, and lists