【作者】 朱耿灿；

【导师】 王建；

【作者基本信息】 福建师范大学 ， 基础数学， 2009， 硕士

【摘要】 硕士学位论文《不动点理论及Mazur-Ulam等距定理的一些探讨》综合运用Banach空间几何理论和算子方面的知识。全文共分如下三个章节:第一章为绪论。主要介绍本文的研究背景及相关的一些预备知识,并且给出文中所涉及的大部分概念和记号。第二章中,研究了赋β-范空间中渐近伪压缩和渐近非扩张映象的不动点迭代逼近问题,证明了渐近伪压缩映象T的修改的Ishikawa迭代序列收敛到不动点的充要条件。第三章中,研究了在赋2-范空间(更一般地,在2-距离空间)框架下有关不动点理论以及相关的问题,运用Picard迭代序列逼近的方法证明了压缩型映象有唯一不动点,进而也讨论了Picard迭代序列的稳定性。第四章中,探讨了在赋(2,p)范空间中的Mazur-Ulam问题,考虑用其他条件来替代“满射”这个条件。更多还原

【Abstract】 Master paper "some fixed point theorems and isometric theorem in linear 2-normed space" ,which based on the formers’studies, applies the geometric theory of Banach space and the operator theory comprehensively. The whole paper is divided into three chapters.The first chapter of the paper starts from the preliminary and some basic theorems and results . Also,we introduce some conceptions and notations needed in the following chapters.In Chapter 2, we constructed a new Ishikawa iteration precess inβ-normed linear Space, and we prove a sufficient and necessary condition for the new Ishikawa iteration processes with error of asymptotically pseudo-contractive mapping T to converge to fixed points.In Chapter 3, We first obtain generalizations of the 2-metric space version of some contractive type mappings, and then prove that each such mapping has a unique fixed point. Moreover, this enables us to establish some fixed point theorems in linear 2-normed space. At last we obtain some stability results for Picard iteration in 2-metric space.In Chapter 4, We focus our attention on the Mazur-Ulam problem in linear (2, p)-normed space, and deal with the following problem :instead of surjectivity,what conditions imply the linearity of isometries?更多还原