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...

Given an ill-posed linear operator equation Au = f in a Hilbert space, we formulate a variational problem using Tikhonov regularization with a Sobolev norm of u, and we treat the variational problem by a Sobolev gradient flow. We show that the gradient system has a unique global solution for which the asymptotic limit exists with convergence in the strong sense using the Sobolev norm, and that ...