  Let $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear map on
normed spaces. We say that $f$ is close-to-regular when $f^{t****s}=f^{s****t}$
and $f$ is Aron-Berener regular when all natural extensions are equal. In this
manuscript, we have some results on the Aron-Berner regular maps. We
investigate the relation between Arens regularity of bounded bilinear maps and
Aron-Berner regularity of bounded tri-linear maps. We also give a simple
criterion for the Aron-Berner regularity of tri-linear maps.
