Linear Convergence Study Of Iterative Algorithms For Split Equality Correlation Problems

In 1994,Censor and Elfving abstracted the split feasibility problem from some problems such as phase retrieval and image restoration.This problem has been widely used in many fields,so it has become a hot topic in the field of nonlinear functional analysis and attracted the attention of many scholars.In 2013,Moudafi proposed the split equality problem on the basis of the study of the split feasibility problem.Then,based on the split equality problem,scholars also presented some new problems which are related to the split equality problem.In order to solve the split equality problem and its related problem,people introduced various algorithms and explored the convergence properties of these algorithms.However,almost all of these algorithms are weakly or strongly convergent.We can not get definite convergence rates of these algorithms.But the convergence rates have very important theoretical significance in practical application.This is because if the convergence rates of the algorithms are known,under the conditions of the known errors,we will get iteration times of the algorithms so that the problems are solved by computers.In order to obtain the convergence rates,scholars studied the linear convergence properties of several problems,such as the split feasibility problem,split equality problem and multiple-sets split equality problem.However,the linear convergence properties of most problems which are related to the split equality problem have not been studied by scholars.So they are worth further exploration.In addition,in the process of exploring the linear convergence rates of various algorithms,people utilized the concept of the bounded linear regularity.Yet the bounded linear regularity property is a stronger condition.Therefore,the convergence rates of the split equality problem and its related problems under weaker conditions are also worth further study.This paper mainly researches three problems which are respectively multiple-sets split equality problem,split equality fixed-point problem and split equality mixed equilibrium problem.Firstly,we introduce the concept of the bounded H?lder regularity property by weakening the bounded linear regularity property.And we use this property to prove the sublinear and linear convergence properties of a known algorithm for solving the multiple-sets split equality problem and provide its convergence rates.Secondly,we use the bounded linear regularity property to research the linear convergence properties of the algorithms for solving the split equality fixed-point problem and split equality mixed equilibrium problem,respectively.Finally,we verify our results by numerical experiments and apply the result of the linear convergence of the split equality mixed equilibrium problem to the split equality equilibrium problem,split equality convex minimization problem,split equality mixed variational inequality problem and split equality variational inequality problem.