Research On Bounded Perturbation Resilience Of Algorithms For Split Common Fixed Point Problem

So far,many authors have studied the split feasibility problem(SFP),the split common fixed point problem(SCFPP)and the split variational inclusion problem(SVIP).In their research,CQ algorithm,simple projection method and iterative approximation algorithm have been proposed to solve these problems.Under the appropriate parameter conditions,they prove the weak convergence or strong convergence results of these algorithms.In this paper,the bounded perturbation resilience of the algorithm for solving split common fixed point problems is studied.We propose an inexact viscosity approximation method to solve the split common fixed point problem and consider the bounded perturbation resilience of the proposed method in general real Hilbert space.Under appropriate parameter conditions,the strong convergence and bounded perturbation resilience properties of the proposed algorithm are verified.Furthermore,a generalized viscosity iterative algorithm is proposed to solve the split variational inclusion problem.The algorithm is extended from a compression operator to a cluster of compression operators based on the viscosity iteration algorithm.Under suitable conditions,we prove that the sequences generated by the proposed algorithm converge strongly to the solution of problem and the method has bounded perturbation resilienceproperty.Finally,some numerical examples are given to show the effectiveness and realization of the algorithms.