An accelerate algorithm for the split equality common fixed-point problem of directed operators

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In this paper, we introduce an inertial accelerated algorithm for solving the split equality common fixed-point problem of directed operators in real Hilbert space. Our algorithm includes the simultaneous iterative algorithm as special case which has been proposed by Moudafi and Al-Shemas for solving the split equality common fixed-point problem. We establish a weak convergence theorem for the proposed iterative algorithm, which combines the primal-dual method and the inertial technique. In our algorithm, the step sizes are chosen self-adaptively so that the implementation of the algorithm does not need any prior information about bounded linear operator norms. The efficiency of the proposed algorithm is illustrated by some numerical experiments.