摘 要本文首先介绍 Banach 空间中得不动点定理、在其她线性拓扑空间中不动点定理得一维推广形式、在一般完备度量空间上得推广形式、 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,总结了利用不动点定理求解有关数列得问题、其中包括数列通项、数列得有界性问题、最后介绍了不动点定理中得吸引不动点与排斥不动点在讨论数列得单调性及收敛性方面得应用、关键词 :Banach 不动点定理,数列通项,有界性,单调性,收敛性、AbstractThis article firstly introduced the Fixpoint Theorem in Banach space, the one-dimensional extended form of the Fixpoint Theorem in other linear topological space and the extended form in general plete metric space 、 Then, we summarized the problem on sequence of number using Fixpoint Theorem, analyzing the characteristics of tests emerged on math papers of all parts of our country recent years, including the problem of general term and boundedness of a sequence of number、 At last, attractive fix point and rejection fix point in Fixpoint Theorem were introduced which can solve the problem about the monotonicity and astringency of sequence of number、Keywords:Banach fixed point theorem, Sequence, Boundedness, Monotonicity Convergence、目 录第 1 章 绪论..............................................................................................................................11 、 1 导论 .......................................................................................................................... 3 1 、 1 、 1 选题背景 .................................................................................................... 3 1 、 1 、 2 选题意义 .................................................................................................... 2 1 、 1 、 3 课题讨论内容 ............................................................................................ 3 1 、 2 讨论现状 ....................................
