On the size of approximately convex sets in normed spaces

S. J. Dilworth, Ralph Howard, James W. Roberts

Let X be a normed space. A subset A of X is approximately convex if $d(ta+(1-t)b,A)\le 1$ for all $a,b\in A$ and $t\in [0,1]$ where $d(x,A)$ is the distance of $x$ to $A$. Let $…