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The split equality problem is a generalization of the split feasibility problem, meanwhile it is a special case of multiple-sets split equality problems. In this paper, we propose an iterative algorithm for solving the multiple-sets split equality problem whose iterative step size is split self-adaptive. The advantage of the split self-adaptive step size is that it could be obtained directly from the iterative procedure without needing to have any information of the spectral norm of the related operators. Under suitable conditions, we establish the theoretical convergence of the algorithm proposed in Hilbert spaces, and several numerical results confirm the effectiveness of the algorithm proposed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose an iterative algorithm for solving the split equality common null point problem (SECNP), which is to find an element of the set of common zero points for a finite family of maximal monotone operators in Hilbert spaces. We introduce the concept of bounded linear regularity for the SECNP and construct several sufficient conditions to ensure the linear convergence of the algorithm. Moreover, some numerical experiments are given to test the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the relaxed gradient projection algorithm to solve the split equality problem in Hilbert spaces, and we investigate its linear convergence. In particular, we use the concept of the bounded linear regularity property for the split equality problem to prove the linear convergence property for the above algorithm. Furthermore, we conclude the linear convergence rate of the relaxed gradient projection algorithm. Finally, some numerical experiments are given to test the validity of our results. [ABSTRACT FROM AUTHOR]