Iteration Algorithms For Solving Split Equality Feasibility Problem And Its Extended Problems

In the research field of the nonlinear functional analysis,the split feasibility problem is a hot topic and it is widely used in signal processing,image restoration,etc.The split feasibility problem and its related problems provide theoretical basis and research tools for different spaces problems.Many scholars have devoted to researching these problems.This essay mainly studies the related problems of feasibility problem,including the split equality feasibility problem,the split equality fixed point problem and extended split equality fixed point problem.For every kind of problem,we propose a simultaneous iterative algorithm,respectively and prove the convergence of sequences generated by the iterative algorithm.Some numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms.This essay mainly includes the following several aspects.Firstly we introduce the research background and present situation of the split equality feasibility problem and the split equality fixed point problem,also summarize the preliminary knowledge and the structure arrangement of the paper.Secondly,we mainly study the split equality feasibility problem,propose the relaxed inertial accelerated algorithm and the modified relaxed inertial accelerated algorithm,and prove the weak convergence of sequences generated by the iterative algorithm.We have made the improvement that the selection of stepsize is only dependent on the information of current iterative point,so that the algorithm is easy to perform.Some numerical results are shown to compare the relaxed CQ algorithm,the relaxed inertial accelerated algorithm and the modified relaxed inertial accelerated algorithm.We come to a conclusion that the relaxed inertial accelerated algorithm and the modified relaxed inertial accelerated algorithm are superior to the relaxed CQ algorithm from the point of the iterative number,iterative time and the stability.Once more,we study the split equality fixed point problem and propose an alternating iteration algorithm.In this algorithm,the stepsize is only dependent on the current iteration point information,therefore the new iteration point information can be fully used.Some numerical results are shown to confirm the feasibility of the proposed algorithm.Then we generalize the split equality fixed point problem,present a new iterative algorithm by optimizing the projection space of the algorithm,and prove the convergence of sequences generated by the iterative algorithm.Some numerical results are shown to confirm the efficiency of the proposed algorithm.Finally,the work of this paper and the deficiencies in the study are summarized and the further research field is put forward.