Iterative Algorithms For Solving A Split Equality Fixed Point Problem

Split equality fixed point problem(SEFPP)is a kind of important mathematical problems.And it is also a generalization of the split feasibility problem(SFP).Split equality fixed point problem(SEFPP)as related problems of variational inequality.It has many important applications,such as in signal processing,medical image reconstruction,especially radiation therapy,computer tomography.It has attracted special attention of many scholars.The paper mainly study the iterative algorithm of split equality fixed point problem and generalized nonlinear mixed quasi-variational inequalities,the results as follows:The second chapter mainly studies the iterative algorithm of split equality fixed point problem and its convergence.It is divided into three parts: The first part construct the Ishikawa type iterative algorithm,under the conditions of the mapping is Lipschitz continuous and pseudo-contractive mapping.We proved that the strong convergence and weak convergence of sequences generated by the algorithm.The second part,the mapping is pseudo-contraction without Lipschitz continuious.We construct the Mann type iterative algorithm,and prove the weak convergence of the sequences generated by the algorithm.The three part,in order to avoid calculation of projection mapping.We use nonexpansive mapping instead of projection mapping.We structure the Ishikawa type iterative algorithm,and we obtained the convergence under appropriate conditions.The results improve and develop the corresponding results of some literature.The third chapter mainly studies auxiliary principle and iterative algorithm for a system of generalized nonlinear mixed quasi-variational-like inequalities.Firstly,under the suitable conditions,we show the existence and uniqueness theorem of solution for the system of auxiliary generalized nonlinear mixed quasi-variational-like inequalities by applying the auxiliary principle technique and minimizing sequences of convex function.Second,based on the existence result,we construct a new iterative algorithm.Under the appropriate conditions,both the existence of solutions of the original problem and theconvergence of iterative sequences generated by the algorithm are proved.The results improve and extend some known results.