Effective metastability for a method of alternating resolvents

A generalized method of alternating resolvents was introduced by Boikanyo and Moroanu 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.