  The classical Krasnoselskii-Mann iteration is broadly used for approximating
fixed points of nonexpansive operators. To accelerate the convergence of the
Krasnoselskii-Mann iteration, the inertial methods were received much attention
in recent years. In this paper, we propose an inexact inertial
Krasnoselskii-Mann algorithm. In comparison with the original inertial
Krasnoselskii-Mann algorithm, our algorithm allows error for updating the
iterative sequence, which makes it more flexible and useful in practice. We
establish weak convergence results for the proposed algorithm under different
conditions on parameters and error terms. Furthermore, we provide a
nonasymptotic convergence rate for the proposed algorithm. As applications, we
propose and study inexact inertial proximal point algorithm and inexact
inertial forward-backward splitting algorithm for solving monotone inclusion
problems and the corresponding convex minimization problems.
