【摘要】：不動點問題是泛函分析中主要研究方向之一,并且在代數(shù)方程、微分方程、隱函數(shù)理論等方面有廣泛的應(yīng)用,本文主要從兩個方面研究算子的不動點問題.一方面,通過研究算子本身的性質(zhì)研究算子的不動點問題；另一方面,通過構(gòu)造適當?shù)牡蛄?并研究該序列的收斂性得到算子的不動點.首先,構(gòu)造適當?shù)牡蛄醒芯克阕拥牟粍狱c問題是研究算子不動點問題的重要方法.第一章給出了凸度量結(jié)構(gòu)和滿足(Φ)條件函數(shù)的概念,通過構(gòu)造帶有誤差的廣義Mann型迭代序列探索凸度量空間中弱可共處映射的公共不動點問題.第二章給出了向陽的非擴張映射(sunny nonexpansive mapping)和向陽的非擴張收宿子集(sunny nonexpansive retraction)的概念,隨后我們引入兩個新型的粘滯迭代方法：設(shè)X是一個Banach空間,C和D是X的非空子集,D(?)C.映射P：C→D為向陽型收縮映射.我們構(gòu)造序列{x。},{yn}如下：在這一章中我們將研究這兩種新型粘滯迭代算法產(chǎn)生的迭代序列的收斂性質(zhì).通過研究算子本身的性質(zhì)研究不動點問題是研究不動點問題的另一種方式.第三章介紹D度量空間的概念及基本性質(zhì),并且定義了一種新型的膨脹映射：D-Ⅲ型膨脹映射.在這一部分,我們將在D度量空間中探索D-Ⅲ型膨脹映射的不動點問題和公共不動點問題.
[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，

本文編號：2441409