近年來，在圖像處理與強度可調(diào)輻射療法的實際應用背景下，分裂可行性問題成為近期非線性分析的研究熱點之一。 本專著從三個方面研究分裂可行性問題與廣義分裂可行性問題（分裂公共不動點問題、分裂變分不等式問題和分裂公共零點問題）解的迭代逼近。主要體現(xiàn)在新算法設計、空間擴展和參數(shù)減弱限制條件等方面。對于豐富和擴展分裂可行性問題相關(guān)理論有重要價值。
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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
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