摘要
给出"积分型Cauchy中值函数"的定义,对"积分型Cauchy中值函数"的分析性质进行了系统讨论,证明了"积分型Cauchy中值函数"的单调性、可积性、连续性、可微性等分析性质.作为"积分型Cauchy中值函数"的特例,给出了"第一积分中值函数"的定义及"第一积分中值函数"相应的分析性质.
In this paper, we give the definition of ＂ Cauchy mean value function of integral type＂, discuss the analysing qualities of it, and prove the analysing qualities of its monotonicity, integrability, continuity, differentiability. As a special sample of it, we give the definition of ＂the mean value function for the first integrals＂ and its analysing qualities.
出处
《数学的实践与认识》
CSCD
北大核心
2014年第3期281-286,共6页
Mathematics in Practice and Theory
基金
黑龙江省教育厅科学研究项目(12531841)
关键词
中值函数
单调性
可积性
连续性
可微性
mean value function
monotonicity
integrability
continuity
differentiability
