NEW INERTIAL METHOD FOR NONEXPANSIVE MAPPINGS

There have been increasing interests in studying inertial Krasnoselskii-Mann iterations due to the presence of inertial extrapolation step which improves the rate of convergence of Krasnoselskii-Mann iterations. These results analyzed the convergence properties of inertial Krasnoselskii-Mann iterations and demonstrated their performance numerically on some imaging and data analysis problems. It is discovered that these proposed inertial Krasnoselskii-Mann iterations assumed some stringent conditions on the inertial factor which make the implementations difficult in some numerical examples. In this present paper, we provide a new inertial Krasnoselskii-Mann iteration, prove its weak convergence and the corresponding rate of convergence under some suitable conditions.