文档介绍：学号:0907421032
本科毕业论文(设计)
(2013届)
不动点定理及其应用
院系数学系
专业数学与应用数学
姓名赵云峰
指导教师周永强
职称讲师
摘要
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不动点定理是20世纪数学发展中的重大课题,、拓扑学、非线性分析等多种问题,运用不动点定理,可以解决数学中出现的许多问题,运用此定理可以使问题变的简单,而且此定理使用起来比较方便. 本文首先介绍Banach空间中的不动点定理、在其他线性拓扑空间中不动点定理的一维推广形式、在一般完备度量空间上的推广形式. 其次,通过分析近几年全国各地高考数学卷中一些试题特点,、.
关键词:Banach不动点定理数列通项有界性单调性收敛性.
ABSTRACT
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Fixed point theorem is an important subject in the development of mathematics in the 20th century,its influence throughout the whole theorem in mathematical analysis,topology,nonlinear analysis of a variety of problem, such as,using the fixed point theorem,can solve many problems appeared in this theorem can be the problem es simpler and more convenient to use the paper first introduces fixed point theorem in Banach space,on the other fixed point theorem in linear topological space of one dimensional promotion from,in the general form of promotion on plete metric ,through the analysis of some questions in all over the country in recent years,the college entrance examination mathematics volume characteristic,summarizes the use of the fixed point theorem to solve the the questions about the a series of general term,series boundedness introduces the fixed point theorem in attracting the fixes point and rejection fixed point in discussing monotonicity and convergence of the sequence.
Key words:Banach fixed point theorem monotonicity and convergence general- term series boundedness
目录
摘要 I
ABSTRACT II
1 引言 1
2 关于不动点的研究现状 1
3 不动点定理 2
有关定理 2
不动点定理和几种推广形式 2
4 不动点定理在数列中的应用 4
4
数列的有界性 6
数列的单调性及收敛性 7
5 结束语 11
参考文献 12
1 引言
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不动点理论的研究兴起于20世纪初,,不动点定理有了进一步的发展,,,丹麦数学家尼尔森研究不动点个数问题,、姜伯驹、石根华一些人则大力度推广了可计算尼