On Modified Halpern and Tikhonov–Mann Iterations

Abstract We show that the asymptotic regularity and strong convergence of modified Halpern iteration due to T.-H. Kim H.-K. Xu studied further by A. Cuntavenapit B. Panyanak Tikhonov–Mann introduced H. Cheval L. Leuştean as a generalization an Y. Yao et al. has recently been Boţ can be reduced each other in general geodesic settings. This, particular, gives new proof result together with from Hilbert CAT(0) spaces. Moreover, quantitative rates metastability K. Schade U. Kohlenbach adapted transformed into for corresponding recent results on latter Cheval, Dinis, P. Pinto, respectively. A transformation converse direction is also possible. obtain order O (1/ n ) both (and so particular iteration) setting special choice scalars.