Dynamical and proximal approaches for approximating fixed points of quasi-nonexpansive mappings

In this paper, we derive some weak and strong convergence results for a nonhomogeneous differential equation with a Lipschitz quasi-nonexpansive mapping. We also consider a discrete version that provides an iterative algorithm for approximating a fixed point of the mapping. We state some weak and strong convergence results related to this algorithm. Finally, we compare this algorithm with the classical algorithms for approximating fixed points of quasi-nonexpansive mappings, and show the advantage of the proposed algorithm via convergence rates.