范拓扑

Li 101 proved the nonlinear ergodic theorem for semitopological semigroups of Lipschitzian mappings in the uniformly convex Banach space with the Frechet differentiable norm without using the concept of invariant mean and submean. In Chapter 1, we extend the results in [23 [24] to the case of almost-orbit.

Li［10］避开了不变平均及不变子平均的概念，在具Frechet可微范数的一致凸Banach空间中，给出了一般拓扑半群上渐近非扩张半群的遍历压缩定理。

Ruck, Hirano and Reich extended Baillon抯 theorem to a uniformly convex Banach space with a Frechet differentiable norm. Hirano-Kido-Takahashi, Oka, Park and Jenong proved the ergodic theorem for commutative semigroups of nonexpansive mappings and asymptotically nonexpansive mappings in the uniformly convex I3anach space with the Frechet differentiable nonn.

aillon的定理被Bruck，Hirano及Reich推广到具Frechet可微范数的一致凸Banach空间中，而当G是一般交换拓扑半群时，Hirano-Kido-Takahashi，Oka，Park及Jeong分别给出了具Frechet可微范数的一致凸Banach空间中非扩张半群及渐近非扩张半群的遍历压缩定理和遍历收敛定理。

It is shown that an exponentially bounded integrated bisemigroups can be considered as the integration of a strongly continuous bisemigroup of bounded linear operators in some subspace of a Banach space with stronger norm topology,and also as the restriction of a strongly continuous bisemigroup of bounded linear operators in a bigger space with weaker norm topology.

证明了Banach空间x上的指数有界积分双半群可以作为x的某个子空间上具有较强范数拓扑下的有界线性算子强连续双半群的积分，同时也可作为较大空间上具有较弱范数拓扑下的有界线性算子强连续双半群积分的限制。

The concepts of the S-simplest form of a seminorm family P and the P-reflexive locally convex space are introduced. The seminorm family P and its every S-simplest form generate the same locally convex separated topology on X are proved.

引入半范数族P的S-最简形式和P-自反局部凸空间的概念，证明了半范数族P和它的每一个S-最简形式都生成X上相同的局部凸拓扑。

Let X be a real linear space,P a family of separated seminorms on X and TP the locally convex separated topology on X generated by P.

设X是实线性空间，P是X上的一族分离半范数且Tp是X上由P生成的局部凸分离拓扑。

Among which topology can not be a norm topology.

其中拓扑不可能是范数拓扑。

The relation between the completeness of several local convex topology in normed vector space and that of induction topology of its unit ball was pointed out in this paper.

本文指出了赋范线性空间上的一些局部凸拓扑的完备性与它的单位球上相应的诱导拓扑的完备性之间的关系。

By properties of a real function, fixed points problem on two complete metric spaces are discussed.The result generalizes corresponding result of Fisher.Moreover, this result provides a general convergence rate estimate. Meanwhile, we discuss the existence of fixed point on two normed linear spaces under the condition of weak topology, and we obtain a new fixed point theorem.

利用实函数性质，讨论了两个不同度量空间中两个映象乘积的不动点问题，推广了Fisher的主要结果，并给了出逼近不动点的敛速估计；同时，在弱拓扑的意义下，利用分析的方法，讨论了赋范空间中有关映象不动点的存在性，得到一个新的不动点定理。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。