摘要:数列和函数的上下极限实为数学分析中的基本概念,其等价定义也有几种。本文总结了数列上、下极限的5种等价定义和函数上、下极限的5种等价定义,并利用函数上、下极限的概念来定义广义导数, 将广义导数和Clarke意义下的广义梯度对比。
关键词: 上极限; 下极限; 等价;广义导数
Abstract:The sequence and in the function about limit actually mathematical analysis's basic concept, its equal definition also has several kinds and has given the sequence top and bottom limit 5 kinds of equal definitions and the function top and bottom limit 5 kinds of equal definitions, and defines the generalized derivatives using the function top and bottom limit's concept, under generalized derivatives and Clarke significance generalized gradient contrast.
Key words: Top limit; Bottom limit; Equal; Generalized derivatives
数列和函数的上下极限实为数学分析中的基本概念,其等价定义也有几种,往往在学习和应用的时候造成混乱,作者希望通过该课题的研究对此概念的各种等价定义进行整理,进行相关证明,并利用函数的上、下极限定义广义导数。