On May 10, 2023 at 16:00 EEST, Horațiu Cheval (University of Bucharest) will give a talk in the Proof Mining Seminar.
Title: The Tikhonov-Mann iteration for families of mappings
Abstract: We present recent results from , in which we generalize the strongly convergent Krasnoselskii-Mann-type iteration defined by Boț and Meier in  for finding a common fixed point of a family of nonexpansive operators from Hilbert spaces to the abstract setting of W-hyperbolic spaces, and we compute effective rates of asymptotic regularity for it. This extends at the same time results on the Tikhonov-Mann iteration obtained recently with Ulrich Kohlenbach and Laurențiu Leuștean [2, 3] from single mappings to families of mappings.
 R.I. Boț, and D. Meier. A strongly convergent Krasnosel’skii–Mann-type algorithm for finding a common fixed point of a countably infinite family of nonexpansive operators in Hilbert spaces. Journal of Computational and Applied Mathematics, 395:113589, 2021.
 H. Cheval, U. Kohlenbach, and L. Leuștean. On modified Halpern and Tikhonov-Mann iterations. Journal of Optimization Theory and Applications, 197:233–251, 2023.
 H. Cheval and L. Leuștean. Quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration. Optimization Methods and Software, 37(6):2225–2240, 2022.
 H. Cheval. Rates of asymptotic regularity of the Tikhonov-Mann iteration for families of mappings. arXiv:2304.11366 [math.OC], 2023.
Google Meet link: https://meet.google.com/xwm-syvx-bbr