In this paper, we present the convergence of Krasnoselskii Mann iterative process for common fixed points of pointwise Lipschitzian evolution family of bounded nonlinear operators on a Banach space ℜ .

This article is about investigating Krasnoselskii and Mann’s convergence theorems for nonexpansive evolution family with Bochner integral and without convexity of Banach space. We introduced a general form of these results that extends these results to general form of semigroup called evolution families.