非线性问题的迭代逼近理论
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作者范钦伟，贺慧敏[著]
出版社科学出版社
ISBN9787030740465
出版时间2023-01
装帧平装
开本其他
定价165元
货号12974837
上书时间2024-08-23
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目录
Contents
Part I Split feasibility problem
Chapter 1 Introduction to split feasibility problem 3
1.1 Abstract space and their property 4
1.2 Split feasibility problem 10
1.3 General split feasibility problem 22
1.4 Conclusions 28
Chapter 2 Weak convergence theorems for solving the split feasibility problem 29
2.1 Introduction to split feasibility problem 29
2.2 Preliminaries for weak convergence theorems 36
2.3 Main results 36
2.4 Applications for the theorems 39
2.5 Conclusions 42
Chapter 3 Strong convergence theorems for solving the split feasibility problem 43
3.1 Introduction to the background knowledge 43
3.2 Preliminaries for strong convergence theorems 46
3.3 Main results 47
3.4 Applications for the theorems 51
3.5 Conclusions 54
Chapter 4 Convergence theorems for solving the split common fixed point problem 55
4.1 Introduction to split common fixed point problem 55
4.2 Preliminaries for convergence theorems 57
4.3 Main results 60
4.4 Conclusions 81
Part II Fixed point problems
Chapter 5 Introduction to fixed point problems 85
5.1 Some elementary definitions and properties in Banach space 85
5.2 Some elementary definitions and properties on monotone operator and accretive operator 88
5.3 Brief history on iteration solution of nonlinear operators 90
5.4 Brief history on iteration solution of nonlinear operator semigroups 93
5.5 Conclusions 96
Chapter 6 Fixed point theorems of k-strictly pseudo-contractive mappings in Hilbert space 97
6.1 Introduction to k-strictly pseudo-contractive mappings in Hilbert space 97
6.2 Preliminaries for convergence theorems 102
6.3 Main results 107
6.4 Conclusions 111
Chapter 7 Fixed point theorems of k-strictly pseudo-contractive mappings in Banach space 113
7.1 Introduction to k-strictly pseudo-contractive mappings in Banach space 113
7.2 Preliminaries for convergence theorems 119
7.3 Main results 120
7.4 Conclusions 124
Chapter 8 Common fixed point theorems of asymptotically pseudocontractive semigroups 125
8.1 Introduction to asymptotically pseudo-contractive semigroups 125
8.2 Preliminaries for common fixed point theorems 131
8.3 Main results 132
8.4 Conclusions 136
Part III Equilibrium problems
Chapter 9 Introduction to equilibrium problems 139
9.1 Some elementary definitions and properties 139
9.2 Brief history of equilibrium problems 140
9.3 Conclusions 145
Chapter 10 Convergence theorems for solving equilibrium problems and optimization problems 146
10.1 Introduction to equilibrium problems 146
10.2 Preliminaries for convergence theorems 150
10.3 Main results 154
10.4 Applications for optimization problems 167
10.5 Conclusions 168
Chapter 11 Convergence theorems for equilibrium and fixed point problems 169
11.1 Introduction to equilibrium and fixed point problems 169
11.2 Preliminaries for convergence theorems 171
11.3 Main results 172
11.4 Conclusions 180
Bibliography 181
内容摘要
非线性算子不动点理论是非线性控制理论的重要组成部分,尤其是非线性算子方程(组)解的迭代逼近问题一直是非线性控制理论领域活跃的研究课题.近年来，在图像处理与强度可调辐射疗法的实际应用背景下，分裂可行性问题成为近期非线性分析的研究热点之一。本专著从三个方面研究分裂可行性问题与广义分裂可行性问题（分裂公共不动点问题、分裂变分不等式问题和分裂公共零点问题）解的迭代逼近。主要体现在新算法设计、空间扩展和参数减弱条件等方面。对于丰富和扩展分裂可行性问题相关理论有重要价值。
精彩内容
非线性算子不动点理论是非线性控制理论的重要组成部分,尤其是非线性算子方程(组)解的迭代逼近问题一直是非线性控制理论领域活跃的研究课题.近年来，在图像处理与强度可调辐射疗法的实际应用背景下，分裂可行性问题成为近期非线性分析的研究热点之一。本专著从三个方面研究分裂可行性问题与广义分裂可行性问题（分裂公共不动点问题、分裂变分不等式问题和分裂公共零点问题）解的迭代逼近。主要体现在新算法设计、空间扩展和参数减弱条件等方面。对于丰富和扩展分裂可行性问题相关理论有重要价值。
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