Question

急求英语翻译 谢谢！

不动点的概念是法国数学家 H.Poincar´ e 于1895年至1900年间, 在”庞加莱最后定
理”的证明中首先使用的. 他把限制性三体问题周期解的存在性, 归结为满足某种条件
平面连续变换不动点的存在问题. 1910年, L.E.J.Brouwer 证明了有限维空间中多面体
上的连续映射至少有一个不动点, 从而开启了不动点理论研究的先河. 特别是波兰数学
家 Banach 在1922年使用 Picard 迭代方法证明了 Banach 压缩映射原理后, 由于其结果
的优美性和成功地解决了像隐函数存在定理, 微分方程初值问题解的存在性等一系列重
大应用问题, 使得不动点理论成为数学宝库中的一朵奇葩. 特别是近几十年来, 随着计算
机的发展, 人们使用各种各样的迭代方法去逼近非线性映射的不动点并应用其解决某些
实际问题. 在数学, 物理学等诸多学科上都取得了重要进展, 并日臻完善, 最终成为了非
线性泛函分析理论的重要组成部分.

Answer 1

The concept of the fixed point is the French mathematician H.Poincar E in between 1895 and 1900, the last in the "Poincare
First use ". He put the existence of the periodic solution of the restricted three body problem,attributed to meet certain conditions
Problems of plane transform continuous fixed point. In 1910, L.E.J.Brouwer proved that thepolyhedral finite dimensional space
Continuous mapping on at least one fixed point, which opened the fixed point theory ofprecedent. Especially the Poland mathematics
Banach use the Picard iteration method is proved in 1922 that the Banach contraction mapping principle, because of its results
The beauty and successfully solved as the implicit function theorem, the existence of solutions of initial value problem of differential equation of a series of important
Application of fixed point theory, has become a wonderful work in the treasure house ofmathematics. Especially in recent years, along with the calculation
Machine development, people use a variety of iterative methods to approximate the nonlinearmappings and apply it to solve some
Practical problems. In mathematics, physics and other disciplines have made importantprogress, and to continue to improve, eventually become non
As an important part of the theory of linear functional analysis.