Several Modified Iterative Algorithms And Their Applications For Solving The Split Feasibility Problems In Hilbert Spaces

The main purpose of this paper is to introduce two modified extragradient methods and two modified Ishikawa iteration methods to solve the feasibility problem in Hilbert spaces.We introduce a new composite iterative scheme by using extragradient iteration method,Mann iteration method,Ishikawa iteration method and Halpern iteration method.It is proved that the sequence generated by the iterative scheme converges strongly to the solution of the split feasibility problem C∩A-1(Q)which is the minimum-norm solution.The strong convergence theorem of the corresponding iterative algorithm is given under the appropriate constrains.The results of this paper have improved and developed the corresponding results announced in the existing references.The thesis can be divided into four chapters:In Chapter 1,we recall the research background and development status of the split feasibility problem.We state the main work of this paper.In Chapter 2,We study we introduce two new composite iterative schemes by using extragradient iteration method,Mann iteration method and Halpern iteration method.It is proved that the sequence generated by the iterative scheme converges strongly to the solution of the split feasibility problem C ∩ A-1(Q)which is the minimum-norm solution.In Chapter 3,we study we introduce two new composite iterative schemes by using Ishikawa iteration method,Mann iteration method and Halpern iteration method.It is proved that the sequence generated by the iterative scheme converges strongly to the solution of the split feasibility problem C∩A-1(Q)which is the minimum-norm solution.In Chapter 4,this chapter gives the conclusion and its prospect.