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1·A theorem of synthetic algorithm is proved by local quasi contraction mapping.

对局部拟压缩映射进行了讨论，并得到了关于综合算法的一个定理。

2·Therefore, the Contraction mapping principle in semi-metric space has been proved.

进而证明了半度量空间中的压缩映像原理。

3·Secondly, the existence and uniqueness of the generalized local solution is obtained using the contraction mapping principle.

然后利用压缩映象原理方法，证明了方程局部广义解的存在唯一性；

4·By using the contraction mapping principle, the boundary value problems for a second order functional difference equation are investigated.

利用压缩映照定理，研究了一个二阶泛函差分方程边值问题，得到存在和唯一性定理。

5·In the present paper, we define a generalized degree for A-compact 1-set contraction mapping, the result extends what Zhang Qingyong obtained in 1984.

定义了A-紧1-集压缩映象场的广义度，扩展了1984年张庆雍建立的半紧1-集压缩映射的不动点指数理论。

6·For the randomness of classical GA which appears in calculation process, the contraction mapping GA is applied to make the calculation asymptotically convergent.

对经典的遗传算法在计算中出现的随机性问题，则采用压缩映射遗传算法使计算过程渐近收敛。

7·In this paper, we extend an important fixed point theorem for set-valued. A random fixed-point theorem for random set-valued semi-closed 1-set contraction mapping is obtained.

将集值半闭1 -集压缩映象的一个重要不动点定理随机化，得到随机集值半闭1 -集压缩映象的随机不动点定理。

8·By using the contraction mapping principle, the boundary value problems for a second order functional difference equation are investigated. Existence and uniqueness results are obtained.

利用压缩映照定理，研究了一个二阶泛函差分方程边值问题，得到存在和唯一性定理。

9·Stability of equilibrium in an oligopoly market has important implications. This paper focuses on the stability condition of equilibrium by using contraction mapping and fixed point principle.

在一个由少数制造商控制的市场中，平衡点的稳定性有着重要的应用。本文应用压缩映照及不动点原理给出平衡点稳定的一些条件。

10·Using the contraction mapping principle, we proved a theorem about the existence of solution for initial value problem of a class of implicit ordinary differential equations of the first order.

本文应用压缩映象原理证明了一阶隐式微分方程解的存在唯一性定理。