# Quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration

arXiv: https://arxiv.org/abs/2107.07176 · HTML: https://mlsanity.com/paper/2107.07176/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [Asymptotic regularity of a generalised stochastic Halpern scheme](https://mlsanity.com/paper/2411.04845/) (2024)

## Abstract (arXiv)

In this paper, we compute quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration in W-hyperbolic spaces. This iteration is an extension to a nonlinear setting of the modified Mann iteration defined recently by Bot, Csetnek and Meier in Hilbert spaces. Furthermore, we show that the Douglas-Rachfors and forward-backward algorithms with Tikhonov regularization terms are special cases, in Hilbert spaces, of our Tikhonov-Mann iteration.