凸函数的性质与应用摘要 凸函数的性质在许多数学问题的研究和实际应用里具有极为重要的意义 .但是对于大多数非数学专业的大学生来说凸函数只是一个简单平常的数学理论，并未对凸函数有太多的深入了解，更缺乏对凸函数应用的解读和分析 .论文从凸函数的多种定义开始，引出凸函数的性质.也希望借写论文一方面可以强化概念，揭示凸函数的本质，并且可以充分掌握概念与应用的关系，更加深刻地理解凸函数的应用，以解决问题本质达到处理问题的目的.也希望可以激发大家的逻辑思维，来拓展对解决问题的技能和手段.关键词 凸函数，定义，性质，应用，琴生不等式，赫尔德不等式.Properties and applications of convex functionAbstract The properties of convex function are of great significance in the research and practical application of many mathematical problems. But for most non-mathematics major students, convex function is just a simple and ordinary mathematical theory, not too much in-depth understanding of convex function, more lack of application of convex function interpretation and analysis. It is hoped that the thesis can strengthen the concept, reveal the essence of convex function, grasp the relationship between the concept and application, and understand the application of convex function more deeply, so as to solve the essence of the problem and achieve the goal of dealing with the problem. Also hope to stimulate everyone's logical thinking, to expand the problem-solving skills and means.Key words Convex function,definition,property,application,Jensen ,Holder.目 录引 言................................................................................11 凸函数的定义.........................................................................12 凸函数的判定.........................................................................23 凸函数的性质.........................................................................23.1 运算性质-凸函数..................................................
