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 H...