The authors consider a nonempty closed convex subset

$K$ of a reflexive Banach space

$E$ with a weakly continuous dual mapping, and

${\left\{{T}_{i}\right\}}_{i=1}^{\infty}$, an infinite family of asymptotically nonexpansive mappings with the sequence

$\left\{{k}_{in}\right\}$ satisfying

${k}_{in}\ge 1$ for each

$i=1,2\cdots $,

$n=1,2,\cdots $, and

${lim}_{n\to \infty}{k}_{in}=1$ for each

$i=1,2,\cdots $. They introduce a new implicit iterative scheme generated by

${\left\{{T}_{i}\right\}}_{i=1}^{\infty}$ and prove that the scheme converges strongly to a common fixed point of

${\left\{{T}_{i}\right\}}_{i=1}^{\infty}$, which solves a certain variational inequality.