Part I Split feasibility problem Chapter 1 Introduction to split feasibility problem 1.1 Abstract space and their property 1.2 Split feasibility problem 1.3 General split feasibility problem 1.4 Conclusions Chapter 2 Weak convergence theorems for solving the split feasibility problem 2.1 Introduction to split feasibility problem 2.2 Preliminaries for weak convergence theorems 2.3 Main results 2.4 Applications for the theorems 2.5 Conclusions Chapter 3 Strong convergence theorems for solving the split feasibility problem 3.1 Introduction to the background knowledge 3.2 Preliminaries for strong convergence theorems 3.3 Main results 3.4 Applications for the theorems 3.5 Conclusions Chapter 4 Convergence theorems for solving the split common fixed point problem 4.1 Introduction to split common fixed point problem 4.2 Preliminaries for convergence theorems 4.3 Main results 4.4 Conclusions Part II Fixed point problems Chapter 5 Introduction to fixed point problems 5.1 Some elementary definitions and properties in Banach space 5.2 Some elementary definitions and properties on monotone operator and accretive operator 5.3 Brief history on iteration solution of nonlinear operators 5.4 Brief history on iteration solution of nonlinear operator semigroups 5.5 Conclusions Chapter 6 Fixed point theorems of k-strictly pseudo-contractive mappings in Hilbert space 6.1 Introduction to k-strictly pseudo-contractive mappings in Hilbert space 6.2 Preliminaries for convergence theorems 6.3 Main results 6.4 Conclusions Chapter 7 Fixed point theorems of k-strictly pseudo-contractive mappings in Banach space 7.1 Introduction to k-strictly pseudo-contractive mappings in Banach space 7.2 Preliminaries for convergence theorems 7.3 Main results 7.4 Conclusions Chapter 8 Common fixed point theorems of asymptotically pseudocontractive semigroups 8.1 Introduction to asymptotically pseudo-contractive semigroups 8.2 Preliminaries for common fixed point theorems 8.3 Main results 8.4 Conclusions Part III Equilibrium problems Chapter 9 Introduction to equilibrium problems 9.1 Some elementary definitions and properties 9.2 Brief history of equilibrium problems 9.3 Conclusions Chapter 10 Convergence theorems for solving equilibrium problems and optimization problems 10.1 Introduction to equilibrium problems 10.2 Preliminaries for convergence theorems 10.3 Main results 10.4 Applications for optimization problems 10.5 Conclusions Chapter 11 Convergence theorems for equilibrium and fixed point problems 11.1 Introduction to equilibrium and fixed point problems 11.2 Preliminaries for convergence theorems 11.3 Main results 11.4 Conclusions Bibliography