Research On The Split Equality Fixed Point Problem And Its Extended Forms

In this paper,we study the algorithms for solving the split equality fixed point prob-lem and its extended forms which are widely used in game theory,decision science,equi-librium,image reconstruction,face recognition,etc.Therefore,the research on this subject is of great significance.For solving these problems,we design some new algorithms by the in-depth study on the algorithms in related documents and demonstrate the strong convergence or weak convergence of these algorithms.In the analysis process,we take full use of the definitions of the special operators and its interrelated properties.We verify that the new algorithms have better convergence and faster convergence rate by comparing with the algorithms in related documents by the numerical examples.There are following contents in this paper.Firstly,to solve the split equality fixed point problem,we propose an algorithm by the viscosity technique and prove that the se-quence generated by the algorithm strongly converges to the solution of the split equality fixed point problem.We illustrate the superiority of the algorithm by comparing with pre-vious simultaneous iterative algorithm and alternating iterative algorithm according to numerical examples.Secondly,we study the extended split equality fixed point problem and propose an internal perturbation iterative algorithm.We prove the weak convergence of this algorithm.By numerical examples,we verify the effectiveness of the algorithm.Furthermore,we introduce the extended multi-sets split equality fixed point problem whose operators are L-Lipschitz quasi-pseudo-contractive operators with wide applica-tions.For solving this problem,we present the mixed simultaneous iterative algorithm and select the variational stepsize,which can make the most of the information of the current iteration point.We test and verify effectiveness and stability.Finally,we summarize this paper and put forward the next research direction.