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.

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