关于不动点问题的研究
发布时间：2019-03-16 13:00
【摘要】：不动点问题是泛函分析中主要研究方向之一,并且在代数方程、微分方程、隐函数理论等方面有广泛的应用,本文主要从两个方面研究算子的不动点问题.一方面,通过研究算子本身的性质研究算子的不动点问题；另一方面,通过构造适当的迭代序列,并研究该序列的收敛性得到算子的不动点.首先,构造适当的迭代序列研究算子的不动点问题是研究算子不动点问题的重要方法.第一章给出了凸度量结构和满足(Φ)条件函数的概念,通过构造带有误差的广义Mann型迭代序列探索凸度量空间中弱可共处映射的公共不动点问题.第二章给出了向阳的非扩张映射(sunny nonexpansive mapping)和向阳的非扩张收宿子集(sunny nonexpansive retraction)的概念,随后我们引入两个新型的粘滞迭代方法：设X是一个Banach空间,C和D是X的非空子集,D(?)C.映射P：C→D为向阳型收缩映射.我们构造序列{x。},{yn}如下：在这一章中我们将研究这两种新型粘滞迭代算法产生的迭代序列的收敛性质.通过研究算子本身的性质研究不动点问题是研究不动点问题的另一种方式.第三章介绍D度量空间的概念及基本性质,并且定义了一种新型的膨胀映射：D-Ⅲ型膨胀映射.在这一部分,我们将在D度量空间中探索D-Ⅲ型膨胀映射的不动点问题和公共不动点问题.
[Abstract]:Fixed point problem is one of the main research directions in functional analysis, and it is widely used in algebraic equation, differential equation, implicit function theory and so on. In this paper, the fixed point problem of operators is studied from two aspects. On the one hand, the fixed point problem of the operator is studied by studying the properties of the operator itself, on the other hand, the fixed point of the operator is obtained by constructing an appropriate iterative sequence and studying the convergence of the sequence. Firstly, constructing an appropriate iterative sequence to study the fixed point problem of operators is an important method to study the fixed point problems of operators. In the first chapter, the concepts of convex metric structure and satisfying (桅) conditional functions are given. By constructing a generalized Mann type iterative sequence with errors, the common fixed point problem of weakly coexistent mappings in convex metric spaces is explored. In chapter 2, we give the concepts of Xiangyang nonexpansive mapping (sunny nonexpansive mapping) and Xiangyang nonexpansive boarding subset (sunny nonexpansive retraction). Then we introduce two new viscous iterative methods: let X be a Banach space and C and D be non-empty subsets of X. D (?) C. The mapping P, C, D is a contraction mapping of Yang type. We construct the sequence {x.}, {yn} as follows: in this chapter, we will study the convergence properties of the iterative sequences generated by these two new viscous iterative algorithms. The fixed point problem is another way to study the fixed point problem by studying the properties of the operator itself. In chapter 3, we introduce the concept and basic properties of D-metric space, and define a new type of expansion mapping: d-鈪，
本文编号：2441409
[Abstract]:Fixed point problem is one of the main research directions in functional analysis, and it is widely used in algebraic equation, differential equation, implicit function theory and so on. In this paper, the fixed point problem of operators is studied from two aspects. On the one hand, the fixed point problem of the operator is studied by studying the properties of the operator itself, on the other hand, the fixed point of the operator is obtained by constructing an appropriate iterative sequence and studying the convergence of the sequence. Firstly, constructing an appropriate iterative sequence to study the fixed point problem of operators is an important method to study the fixed point problems of operators. In the first chapter, the concepts of convex metric structure and satisfying (桅) conditional functions are given. By constructing a generalized Mann type iterative sequence with errors, the common fixed point problem of weakly coexistent mappings in convex metric spaces is explored. In chapter 2, we give the concepts of Xiangyang nonexpansive mapping (sunny nonexpansive mapping) and Xiangyang nonexpansive boarding subset (sunny nonexpansive retraction). Then we introduce two new viscous iterative methods: let X be a Banach space and C and D be non-empty subsets of X. D (?) C. The mapping P, C, D is a contraction mapping of Yang type. We construct the sequence {x.}, {yn} as follows: in this chapter, we will study the convergence properties of the iterative sequences generated by these two new viscous iterative algorithms. The fixed point problem is another way to study the fixed point problem by studying the properties of the operator itself. In chapter 3, we introduce the concept and basic properties of D-metric space, and define a new type of expansion mapping: d-鈪，
本文编号：2441409
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