Let X be a normed space and $x_0 \in X$. In this paper we proves the convergence of a convex sequence $x_n = \lambda x_{n−1} +(1−\lambda)f(x_{n−1})$, $\lambda \in (0, 1)$, to the fixed point of the $f$, where $f : X \to X$ is the nonexpansive completely continuous operator, which satisfies some nonexpansive conditions.