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Abstract
In this paper, we investigate and analyse the strong convergence of the sequence generated by an inexact proximal point method with possible unbounded errors for finding zeros of monotone operators in Hadamard spaces. We show that the boundedness of the generated sequence is equivalent to the zero set of the operator to be nonempty. In this case, we prove the strong convergence of the generated sequence to a zero of the operator. We also provide some applications of our main results and give a numerical example to show the performance of the proposed algorithm.
Acknowledgments
The authors are grateful to the Editor and the anonymous referees for their constructive comments leading to the improvement of the paper. This work was done while the second author was visiting the University of Texas at El Paso. The second author would like to thank Professor Djafari Rouhani and the Department of Mathematical Sciences for their kind hospitality at the University of Texas at El Paso during his visit.
Disclosure statement
No potential conflict of interest was reported by the author(s).