Convergence Analysis Of Iterative Algorithms For The Split Feasibility Problem In Metric Spac

The split feasibility problem and split equality problem have many applications in our real life,such as image restoration,signal processing and healthcare,so it is more important to consider the problems.Previous scholars have proposed corresponding algorithms for the problems and prove their convergence.On the one hand,there are a few results on the cross common solutions of these two kinds of problems and their generalized problems.The known iterative algorithms for solving the common solutions of these two kinds of problems are weakly convergent.Based on this phenomenon,we propose an iterative algorithm for multiple-sets split feasibility problem(MSSFP for short)and split equality fixed point problem(SEFPP for short)for firmly quasi-nonexpansive or nonexpansive mappings in infinite dimensional Hilbert spaces,and prove the strong convergence of the algorithm.The algorithm converges to the minimal norm solution of the problem.Finally,numerical experiments show the effectiveness of our iterative algorithm.On the other hand,for solving the split feasibility problem or split equality problem,many iterative algorithms have been proposed by scholars,they are all based on the goal of having fewer iteration steps and shorter iteration times.In view of this,we use the explicit extragradient-like method to solve the split feasibility problem and obtain the fine results.The strong convergence of the algorithm is proved,and the algorithm converges to the minimal norm solution of the problem.Similarly,numerical experiments show that our iterative algorithm is superior to previous ones in terms of iteration steps and iteration time.Finally,since Banach space setting sometimes allows a more realistic modelling of problems arising in applications from industry and natural sciences,we need to introduce the split eqality problem into Banach spaces.Note that inner product plays a key role in proving the convergence of iterative algorithms in Hilbert spaces and not all Banach spaces have inner product.Based on the reasons,we solve the split equality problem by using contractive projection method and pairing method,and obtain the strong convergence of the proposed algorithm under two different step sizes.