DOI: 10.24193/fpt-ro.2024.1.05

Authors: Bruno Dinis and Pedro Pinto

Abstract: A generalized method of alternating resolvents was introduced by Boikanyo and Moroșanu as a way to approximate common zeros of two maximal monotone operators. In this paper we analyse the strong convergence of this algorithm under two different sets of conditions. As a consequence we obtain effective rates of metastability (in the sense of Terence Tao) and quasi-rates of asymptotic regularity. Furthermore, we bypass the need for sequential weak compactness in the original proofs. Our quantitative results are obtained using proof-theoretical techniques in the context of the proof mining program.

Key Words and Phrases: Alternating resolvents, maximal monotone operators, proximal point algorithm, metastability, proof mining, fixeed point.

2010 Mathematics Subject Classification: 47J25, 47H05, 47H09, 47H10, 03F10.

Published on-line: February 1st, 2024.

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