Inertial proximal point algorithm for the split common solution problem of monotone operator equations

Ngày đăng: 17/10/2023

This paper provides a new approach to solving the class of split problems. More precisely, we investigate the split common solution problem for monotone operator equations in real Hilbert spaces. To find a solution to this problem, we propose three new iterative algorithms. These algorithms are established based on the inertial proximal point algorithm. We prove the weak convergence of the first algorithm. Next, to obtain the strong convergence theorems, in the second and the third ones, we combine the first algorithms with the hybrid projection method or the shrinking projection method, respectively. Some applications of the main theorems for solving related problems are also presented. Two numerical examples are also given to illustrate the effectiveness of the proposed algorithms.