面积积分平均的对数凸性
Logarithmic Convexity of Area Integral Means
DOI: 10.12677/PM.2022.125085, PDF,   
作者: 段玉聪：河北工业大学理学院，天津
关键词: 凸性；对数凸性；解析函数；Convexity； Logarithmic Convexity； Analytic Function
摘要: 函数的凸性作为一种非常重要的几何性质，在证明不等式当中，函数的凸性发挥着重要作用。令H(D)表示D上所有解析函数构成的空间，f∈H(D)。解析函数f的加权面积积分平均定义为Mp,a(f,r)。本文主要研究对数凸函数，证明在什么条件下，Mp,a(f,r)是对数凸函数。使得之前论文中的证明步骤变得简化。
Abstract: As a very important geometric property, the convexity of a function plays an important role in proving inequalities. Let H(D) denote the space formed by all analytic functions on D, f∈H(D). The weighted area integral average definition of the analytic function f is Mp,a(f,r). This paper mainly studies the logarithmic convex function, and proves under what conditions, Mp,a(f,r) is a logarithmic convex function. This simplifies the proof steps in the previous paper.
文章引用：段玉聪. 面积积分平均的对数凸性[J]. 理论数学, 2022, 12(5): 749-756. https://doi.org/10.12677/PM.2022.125085

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