Iterative Algorithm Of Nonexpansive Mapping And The Application In Split Equality Problem

The theory of fixed points is an important topic of morden mathematics and it is widely used in many subjects such as optimization and control theory,nonlinear operator etc.Many scholars have devoted themselves to the validity and practicability of the iterative algorithm of nonexpansive operator,but few have studied the convergence speed of the algorithm.Therefore,the study of the inertial correction algorithm will further enrich the theoretical results of the iterative algorithm for non-expansion operators and is of great significance to solving practical problems.In recent years,the research division algorithm and convergence equation problems,has become the optimization problem of a main direction at home and abroad.The current work focus on construction algorithm,the main research more feasible,faster convergence algorithm,and various improvement techniques,split equation more realistic meaning to resolve the problem,so as to expand the application range of the algorithm.Based on the fixed point theory and the mathematical tools such as metric projection and theta method,the historic background and the research status of the fixed point theory are recalled briefly and the summary of the work in this paper is given.We introduce the relaxation projection algorithm into the alternate CQ algorithm,and construct two alternative projection algorithms,which are applied to the horizontal set constraint splitting equation problem,and verify the weak convergence of the algorithm.