  We investigate the 2-center problem for arbitrary strictly convex, centrally
symmetric curves instead of usual circles. In other words, we extend the
2-center problem (from the Euclidean plane) to strictly convex normed planes,
since any strictly convex, centrally symmetric curve can be interpreted as
(unit) circle of such a normed plane. Thus we generalize the respective
algorithmical approach given by J. Hershberger for the Euclidean plane. We show
that the corresponding decision problem can be solved in $O(n^2\log\, n)$ time.
In addition, we prove various theorems on the notions of ball hull and ball
intersection of finite sets in strictly convex normed planes, which are
fundamental for the 2-center problem, but also interesting for themselves.
