TY - JOUR
T1 - A Note on Upper Convex Density
AU - Yin , Jiandong
AU - Zhou , Zouling
JO - Communications in Mathematical Research 
VL - 4
SP - 361
EP - 368
PY - 2021
DA - 2021/05
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19132.html
KW - self-similar set, open set condition, upper convex density.
AB - <p style="text-align: justify;">For a self-similar set $E$ satisfying the open set condition, upper convex
density is an important concept for the computation of its Hausdorff measure, and
it is well known that the set of relative interior points with upper convex density 1
has a full Hausdorff measure. But whether the upper convex densities of $E$ at all
the relative interior points are equal to 1? In other words, whether there exists a
relative interior point of $E$ such that the upper convex density of $E$ at this point is
less than 1? In this paper, the authors construct a self-similar set satisfying the open
set condition, which has a relative interior point with upper convex density less than
1. Thereby, the above problem is sufficiently answered.</p>