A Rate of Metastability for the Halpern Type Proximal Point Algorithm

Using proof-theoretical techniques, we analyze a proof by Hong-Kun Xu regarding result of strong convergence for the Halpern type proximal point algorithm. We obtain rate metastability (in sense Terence Tao) and also asymptotic regularity iteration. Furthermore, our final quantitative bypasses sequential weak compactness argument present in original proof. This elimination is reflected extraction primitive recursive information. work follows from recent results Proof Mining removal arguments.