Quadratic rates of asymptotic regularity for the Tikhonov–Mann iteration

Abstract

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 Boţ, Csetnek and Meier in Hilbert spaces. Furthermore, we show that the Douglas–Rachford and forward-backward algorithms with Tikhonov regularization terms are special cases, in Hilbert spaces, of our Tikhonov–Mann iteration.