Research On Iterative Methods Of Splitting Problems

In the Hilbert space,an iterative algorithm for solving the split common fixed point problem of demicontractive operators is presented.By virtue of this fixed point method,we construct an iteration based on Mann's method for solving the split common fixed point problem of demicontractive operators.Weak convergence analysis is given under some mild assumptions.An iterative algorithm is presented for finding the fixed points of a quasi-asymptotic_pseudo-contraction in Hilbert spaces.It is shown that the proposed algorithm converges strongly to the fixed point of a quasi-asymptotic pseudo-contraction.The split variational inequality problem under a nonlinear transformation has been considered.An iterative algorithm is presented to solve this split problem.Strong convergence results are obtained.This paper divides five parts:The first part,we introduce the development course of fixed point theory,and the research status and significance of several class of split problem.The second part is on the premise of the Hilbert space,the existing algorithm for solving demicontractive operators is improved on the basis of the fixed point algorithm,in this paper,the iterative algorithm is proposed for solving the demicontractive operators split common fixed point problems,and proved the weak convergence of the algorithm by some assumptions.In the third part,we introduced the quasi-asympototic pseudo-contraction fixed point problems in the Hilbert space,on the basis of existing achievements,the iterative algorithm is proposed in this paper,under some appropriate assumptions,prove the strong convergence of the iterative algorithm.The forth part,we introduce an iteration algorithm for solving the split variational inequality problem under a nonlinear transformation,and obtain the strong convergence results.The fifth part is an overview of this article and the prospect of the related work in the future.I hope that the research methods of such problems are becoming more and more general and the requirements are more general.