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In chapter 2, we first give a generalized type of the Prigons fixed point theorem and a straightforward proof of it. At the same time, we give a positive answer to an open question about convergency of iterative sequence for generalized contraction which is bring forwarded by Frigon in [3]. Secondly, by using the introduced function φ, we establish some fixed point theorems for the set-valued φ-contraction mappings in gauge spaces. These results unify and generalize the corresponding results of Cain and Nashed [1], Figon [3], Espinola and Kirk[4], Tarafder [5] et al.

第二章，首先给出Frigon不动点定理[3]的推广及其简洁证明，同时对Frigon在文[3]中提出的关于广义压缩迭代序列收敛性的公开问题给出肯定的回答；然后，通过引入φ函数，在度规空间上建立集值φ-压缩映射的不动点定理，统一并推广了Cain和Nashed[1]，Figon[3]，Espinola和Kirk[4]，Tarafder[5]等的相应结果。

Here, we will give an independent proof of the existence for inequality (2.1.3), and by the way, give an estimate on the width of the bi-enclosing annulus of closed convex curves in the plane. Secondly, in this part, we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane, and investigate the relationship between the embeddedness of the curve and its average geodesic curvature.

其次，对双曲平面上的曲线引入平均测地曲率的概念，并讨论双曲平面上凸曲线的嵌入性与它的平均测地曲率之间的关系，其目的是为了将双曲平(来源：ABC论84文网www.abclunwen.com)面上曲线的性质与欧氏平面中曲线的性质作一些对比；最后，我们利用Minkowski支撑函数构造了一类新的非圆的光滑常宽曲线，其目的是想回答有关常宽曲线的一些未解决问题如是否存在非圆的多项式常宽曲线？

Tom Sawyer stepped forward with conceited confidence and soared into the unquenchable and indestructible "Give me liberty or give me death" speech, with fine fury and frantic gesticulation , and broke down in the middle of it.

汤姆 -索亚十分自信地走上前去，背起了那千古名篇《不自由，毋宁死》。他慷慨陈词，不时还大幅度地做着手势，可背着背着中途就接不上了。

Tom Sawyer stepped forward with conceited confidence and soared into the unquenchable and indestructible "Give me liberty or give death" speech, with fine fury and frantic gesticulation, and broke down in the middle of it.

汤姆？索亚自负地满怀信心走上前去，气势雄壮地背诵那热情奔放、锐不可挡的"不自由，毋宁死"那篇演说，他慷慨激昂地背诵着，还做了些疯狂的手势，可是背到当中就接不下去了。

You should try to give an impression of an efficient ,friendly, progressive company eager to give good service .

你应该努力帮公司树立一种高效率，具有亲和力，不断进取并乐于提供上乘服务的形象。

And you give yourself away, and you give yourself away.

而你放弃了你自己，而你放弃了你自己。

Give yourself credit for your strengths and your individuality. Do not always give in to other people.

你应该对自己的能力和人性有足够的信心，不要总是让步于他人。

As long as you give me credit and promote my works, I'll give you my software.

只要你承认并推广我的工作，我就会给你使用软件。

Give ear, you wise, to my words; and you who have knowledge, give attention to me

你们智慧人，要听我的话。有知识的人，要留心听我说。

This contrast can give emphasis to certain areas and/or give the impression of depth.

这种反差可以给一些重点领域和/或给人深刻。

You can do some assertiveness training.

你可以进行一些自信训练。

We were well on the path to making a rear-wheel-drive global platform," says Mays."

我们正致力于建立一个后轮驱动的平台，"Mays这样说道。"