Abstract
In this paper, we propose a parameterized variable metric three-operator algorithm for finding a zero of the sum of three monotone operators in a real Hilbert space. Under some appropriate conditions, we prove the strong convergence of the proposed algorithm. Furthermore, we propose a parameterized variable metric three-operator algorithm with a multi-step inertial term and prove its strong convergence. Finally, we illustrate the effectiveness of the proposed algorithm with numerical examples.
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