Iterative Algorithms For Variational Inequalities And Minimum-norm Fixed Point In Hilbert Spaces

The paper mainly studies the iterative algorithms for variational inequalities and minimum-norm fixed point in Hilbert spaces. The paper includes five chapters.The first chapter as an introduction, introducing the development background of the problems we study and the present situation, giving the research work and results of this paper.In the second chapter,introducing a new Noor three-step iterative algorithm.We prove a strong convergence theorem for the iterative sequences under some mild conditions. Also,we get two corollaries as the special cases of our theorem.For corollary one,we let S ≡0,F ≡I,then the variational inequalities problem is just the minimum-norm fixed point problem.For corollary two,the mapping in the theorem is more special. we let S ≡0,F ≡ I,and T =I-αAT(I- PQ)A,we attach this problem to split feasibility problems.In the third chapter, introducing a new iterative scheme with Wnmappings, proving a strong convergence theorem for the iterative sequences generated by the algorithm. Also,we get a corollary as the special case of our theorem.For the corollary,we let S ≡0,F ≡ I,in the theorem.Then the variational inequalities problem is just the minimum-norm fixed point problem.In the forth chapter, introducing a new Noor three-step iterative algorithm with Wn mappings.We prove a strong convergence theorem for the iterative sequences under some mild conditions. Also,we get a corollary as the special case of our theorem.For the corollary,we let S ≡0,F ≡ I,in the theorem.Then the variational inequalities problem is just the minimum-norm fixed point problem.Finally, the conclusion is showed in the fifth chapter, and some problems we need to study later are given.