Let $K$ be a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space $E$ with $P$ as a nonexpansive retraction. Let $T_1,T_2,\ldots,T_N:K\longrightarrow E$ be $N$ asymptotically nonexpansive nonself mappings with sequences $\{r^i_n\}$ such that $\sum_{n=1}^{\infty}r^i_n<\infty$, for all $1\leq i\leq N$ and $F=\cap^N_{i=1}F(T_i)\neq \phi$. Let $\{\alpha^i_n\}$, $\{\beta^i_n\}$ and $\{\gamma^i_n\}$ are sequences in [0,1] with $\alpha^i_n+\beta^i_n+\gamma^i_n=1$ for all $i=1,2,\ldots,N$. From arbitrary $x_1\in K$, define the sequence $\{x_n\}$ iteratively by (6), where $u^i_n$ are bounded sequences in $K$ with $\sum_{n=1}^{\infty}u^i_n<\infty$. (i) If the dual $E^*$ of $E$ has the Kadec--Klee property, then $\{x_n\}$ converges weakly to a common fixed point $x^*\in F$; (ii) if $\{T_1,T_2,\cdots,T_N\}$ satisfies condition (B), then $\{x_n\}$ converges strongly to a common fixed point $x^*\in F$.