几类算子公共不动点的存在唯一性问题研究

发布时间：2018-01-16 16:34

本文关键词：几类算子公共不动点的存在唯一性问题研究　出处：《杭州师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：关于度量空间中多个映象的公共不动点的存在性和唯一性问题,已被许多相关数学作者深入研究,获得了一系列有重要意义的结果。本文的研究内容分别涉及到广义度量空间、乘积度量空间、偏度量空间中的一些公共不动点的存在性与唯一性问题,特别地还讨论了拟偏b-度量空间中的耦合重合点和公共耦合不动点问题。本文的目的,就是在更广泛意义下的度量空间中对已有的结果进行扩展延伸,并通过引进新的概念、使用新的方法,研究更为广泛映象类的公共不动点问题。因此本文的相关研究结果具有十分重要的意义。本论文分为五章：第一章,主要介绍了广义度量空间、乘积度量空间、偏度量空间和拟偏b-度量空间中不动点理论和耦合不动点理论的研究背景和研究现状分析。第二章,本章节的研究内容是在广义度量空间的框架下,讨论了三对映象的公共不动点问题,在只要求两对映象满足公共(E.A)性质的条件下,证明了三对映象公共不动点的存在性和唯一性。而且最后给出实例说明我们得到的新结果的有效性。我们的结果不同于当前的已知结果。第三章,本章节在完备的乘积度量空间中,讨论了两对弱交换映象的公共不动点问题,证明了几个新的公共不动点定理。第四章,本章节在偏度量空间中构造了一种新型ψ型压缩条件,讨论了满足这种新型压缩条件下的两对弱相容映象的公共不动点问题,证明了两对映象公共点的存在性与唯一性,并给出了满足定理条件的实例,用以说明定理的有效性。第五章,本章节的研究内容是在有两个拟偏b-度量的拟偏b-度量空间中,探讨非线性映象的耦合重合点及公共耦合不动点的存在性与唯一性问题,并证明了一些新的不动点定理,最后给出了实际例子支撑我们所得的新结果。
[Abstract]:The existence and uniqueness of common fixed points of multiple mappings in metric spaces have been deeply studied by many mathematical authors. A series of important results are obtained. In this paper, we discuss the existence and uniqueness of some common fixed points in generalized metric space, product metric space and partial metric space respectively. In particular, we also discuss the problem of coupling coincidence points and common coupling fixed points in quasi-biased b-metric spaces. The purpose of this paper is to extend the existing results in the more general sense of metric spaces. By introducing new concepts and using new methods, we study the common fixed point problems of more extensive mapping classes. Therefore, the research results of this paper are of great significance. This paper is divided into five chapters: chapter 1. This paper mainly introduces the research background and current situation of fixed point theory and coupled fixed point theory in generalized metric space, product metric space, partial metric space and quasi-partial b metric space. Chapter 2. In this chapter, we discuss the common fixed point problem of three pairs of mappings under the framework of generalized metric spaces, under the condition that only two pairs of mappings satisfy the properties of common mappings. The existence and uniqueness of common fixed points of three pairs of mappings are proved. Finally, an example is given to illustrate the validity of the new results. Our results are different from the known results. Chapter 3. In this chapter, we discuss the common fixed point problem of two pairs of weakly commutative mappings in complete product metric spaces, and prove several new common fixed point theorems. Chapter 4th. In this chapter, we construct a new type 蠄 contraction condition in a partial metric space, and discuss the common fixed point problem of two pairs of weakly consistent mappings satisfying this new contraction condition. The existence and uniqueness of common points for two pairs of mappings are proved, and an example satisfying the theorem conditions is given to illustrate the validity of the theorem. Chapter 5th. In this chapter, we discuss the existence and uniqueness of coupling coincidence points and common coupled fixed points of nonlinear mappings in quasi partial b metric spaces with two quasi partial b metric. Some new fixed point theorems are proved. Finally, some practical examples are given to support our new results.
【学位授予单位】：杭州师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O177.91

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