Iterative Algorithms Of The Split Feasibility Problems And The Split Equality Problems

As the split feasibility problem and the split equality problem have important applications in medicine,signal processing and other fields,they attracted the attention and study of many authors.They are still the hot topics of nonlinear functional analysis and computational mathematics.In this paper,the author presents new algorithms for solving the split feasibility problem,the split common fixed-point problem of averaged operators and the split equality common fixed-point problem and the multiple-set split equality problem of firmly quasi-nonexpansive operators,and get the main contents are as follows:Firstly,we use the dual variable to construct the primal-dual algorithm and obtain the weak convergence of the algorithm.Then we adapt the general alternative regularization method to modify the primal-dual algorithm,and obtain the strong convergence of the algorithm.And numerical examples are presented to show the effectiveness of the proposed algorithm.Secondly,we introduce the primal-dual algorithm to solve the split common fixed-point problem of averaged operators,and obtain the weak convergence of the algorithm.Then we adapt the viscosity approximation method to modify the primal dual algorithm,and obtain the strong convergence of the algorithm.Thirdly,we present the self-adaptive algorithm to solve the split equality common fixed-point problem of firmly quasi-nonexpansive operators,and obtain the weak convergence of the algorithm.Then we adapt the viscosity approximation method to modify the self-adaptive algorithm,and obtain the strong convergence of the algorithm.Fourthly,we introduce two self-adaptive algorithms of mixed cyclic and parallel to solve the multiple-set split equality problem of firmly quasi-nonexpansive operators,and obtain the weak convergence of the algorithms.