压缩映射

Firstly, we prove the existence and uniqueness of the adapted solution of multi-dimensional backward stochastic differential equations driven by Brownian motion and Lévy process by using predictable representation theorem and the fixed point theorem about contract mapping, and also prove the comparison theory.

第一部分运用可料表示定理和压缩映射原理证明由布朗运动和Lévy过程共同驱动的多维倒向随机微分方程适应解的存在唯一性及其相应的比较定理。

One of Hutchinson's basic results is: If {S〓,…, S〓} is a family of contract operators on a complete metric space, then there is a unique nonempty compact set K, such that K=〓.

Hutchinson的一个基本结论是：对于完备距离空间上的任一族有限压缩映射{S〓，…，S〓}，存在唯一的不变非空的紧集合K，〓。

Also, by using exponential dichotomy, contraction map theorem and matrix theory, some sufficient conditions are obtained to ensure the existence and global exponential stability of almost periodic solution for MAM neural network with distributed delays.

利用矩阵的谱半径、指数二分法结合运用压缩映射原理获得了分布时滞多向联想记忆神经网络模型概周期解的存在性，并在相同条件下证明了概周期解的全局指数稳定性。

A sufficient condition is obtained to ensure the existence and uniqueness of almost periodic solution for MAM neural network with time-varying delays by way of exponential dichotomy and contraction map theorem. Moreover, the global exponential stability of the almost periodic solution for this type of MAM neural network is proved by using Halanay inequality.

利用指数二分法结合运用压缩映射原理获得了变时滞多向联想记忆神经网络模型概周期解的唯一存在性，利用Halanay不等式证明了变时滞多向联想记忆神经网络概周期解的全局指数稳定性。

A integral equation formulation is derived based on modified Green's operator with norm less or equal to one. The integral equation is convergent for any conductivity distribution and frequency if iterative solvers are used.

利用范数小于或等于1的修正Green算子得到各向异性地层中的新积分方程，由于满足压缩映射条件，该积分方程在任意参数条件下总是迭代收敛的。

By a fixed point method,we prove local existence and uniqueness.

利用压缩映射不动点方法证明了局部解的存在唯一性。

It is proved that a generalized Ishikawa type iteration sequence convergences to the unique common fixed point of its more generalized quasi-contractive mapping sequence respect to p.

证明了广义Ish ikawa型迭代序列收敛于关于p的更广义拟压缩映射序列的唯一公共不动点。

In complete convex metric spaces , we use Ishikawa iterative process to approximate common fixed point of quasi - contractive mapping pair.

在完备凸度量空间中，运用广义的Ishikawa迭代序列列逼近拟压缩映射对的公共不动点。

Firstly, by constructing the Lyapunov function with a special structure, a prior estimate is obtained. Secondly, with the help of Green\'s function, the original problem is transformed into an equivalent operator equation, and the fixed point theory of contraction mapping in a Banach space guarantees the existence and uniqueness of the global solution.

首先，构造具有特殊结构的Lyapunov函数，得到解的先验估计；其次，借助Green函数将原方程等价变换成算子方程，Banach压缩映射的不动点定理保证了全局解的存在唯一性；最后通过常微分方程的定解，证明了主要结论，即平凡解全局渐近稳定。

A integral equation formulation is derived based on modified Green's operator with norm less or equal to one.

利用范数小于或等于1的修正Green算子得到各向异性地层中的新积分方程，由于满足压缩映射条件，该积分方程在任意参数条件下总是迭代收敛的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。